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ุจุงุณู… ุงู„ู„ู‡ ุงู„ุฑุญู…ู† ุงู„ุฑุญูŠู… ุงู„ุญู…ุฏ ู„ู„ู‡ ุฑุจ ุงู„ุนุงู„ู…ูŠู†
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ูˆุงู„ุตู„ุงุฉ ูˆุงู„ุณู„ุงู… ุนู„ูŠ ุณูŠุฏู†ุง ู…ุญู…ุฏ ูˆุนู„ูŠ ุฃู‡ู„ูŠ ูˆุตุญุจูŠ
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ูˆุณู„ู… ุฃุฌู…ุนูŠู† ููŠ ุงู„ุจุฏุงูŠุฉ ุจู†ุฑุญุจ ุฌู…ูŠุน ุงู„ุฅุฎูˆุฉ ุงู„ุฃุฎูˆุงุช
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ูˆุงู„ุทุงู„ุจุงุช ููŠ ู…ุตุงู‚ business statistics ููŠ ุงู„ูุตู„
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ุงู„ุฏุฑุงุณูŠ ุงู„ุชุงู†ูŠ ุงู„ู„ูŠ ุงู† ุดุงุก ุงู„ู„ู‡ ุงุชุนู„ุญ ููŠู‡ ู‡ู†ุณุชุฎุฏู…
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.. ู‡ุงูŠ ุงู„ูƒุชุงุจ business statistics ู…ูˆุฌูˆุฏ ููŠ ุงู„ู…ูƒุชุจุฉ
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ุงู„ุขู† ู‡ูŠ ู…ูƒุชุจุฉ ุงู‚ุฑุฃ ุงู„ .. ุฒูŠ ู…ุง ุญูƒูŠุชู‡ ุงู„ู…ุฑุฉ ูุงุชุฑุฉ
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ุงู„ูƒุชุงุจ ููŠู‡ ุงู„ bar point ุจุงู„ูƒุงู…ู„ู„ู„ seven chapters
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ู‡ู… ุชู„ุงุชุฉ ูˆ ุณุชุฉ ูˆ ุณุจุนุฉ ูˆ ุชุณุนุฉ ูˆ ุนุดุฑ ุงูˆ ูˆุงุญุฏ ุนุงุด ูˆ
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ุงุชู†ุงุด ู‡ุฏูˆู„ ุงู„ seven chapters ู‡ู†ุงุฎุฏู‡ู… ุฒุงุฆุฏ ุญุทูŠุช ุงู„
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practice ู„ูƒู„ chapter ู…ูˆุฌูˆุฏ ุฒุงุฆุฏ ุงู„ previous exams
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ุญุทูŠุช ุงุฑุจุน ุงู…ุชุญุงู†ุงุช ู„ู†ูุณ ุงู„ course ู„ู†ูุณ ุงู„ูƒุชุงุจ ุทุจุนุง
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ููŠ ุงู…ุชุญุงู†ุงุช ุชุงู†ูŠุฉ ู‡ุญุทู‡ุง ุนู„ู‰ ุงู„ุตูุญุฉ ุงู† ุดุงุก ุงู„ู„ู‡ุจุฑุถู‡
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ู‡ุญุทู„ูƒ PDF ูˆ ุงู„ PowerPoint ูƒุงู…ู„ุฉ ู‡ุญุทู„ูƒ ููŠู‡ุง
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PowerPoint file ุฒูŠ ุงู„ PDF ู„ูˆ ุญุจูŠุช ุชู‚ุฑุฃ ู…ู†ู‡ุง ุนู„ู‰
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ุงู„ุฌูˆุงู„ ุนู„ู‰ ุงู„ laptop ููŠ ุฃูŠ ู…ูƒุงู† ูŠูƒูˆู† ุนู†ุฏูƒ ุดุบู„ุชูŠู†
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hard copy ุฒูŠ ู‡ูŠูƒ ูƒูˆูŠุณ ูˆ ุงู„ soft copy ุชูƒูˆู† ู…ูˆุฌูˆุฏุฉ
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ู…ุนุงูƒ ุทุจุนุง ุงู„ soft copy ุฃู†ุง ุนุงูŠุฒู‡ุง ููŠ ุงู„ู…ุญุงุถุฑุฉ ู‡ู†ุง
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ุจุญูŠุซ ุฃู†ู‡ ูˆ ุฃู†ุง ุจุดุฑุญ ุญูŠู† ุชูƒุชุจ ุดูˆูŠุฉ ู…ู„ุงุญุธุงุช ูŠุนู†ูŠ
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ุจุชุนู…ู„ notes ุฅู„ูŠูƒ ุฒูŠุงุฏุฉ ู„ุฃู†ู‡ ุบุงู„ุจุง ุงู„ notes ุงู„ู„ูŠ ููŠ
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ุงู„ PowerPoint ู…ุด ูƒุงู…ู„ุฉุจุชุญุท ุดูˆูŠุฉ ุดุบู„ุงุช ุนู„ูŠู‡ุง ุงู„ูŠูˆู…
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ุฅู† ุดุงุก ุงู„ู„ู‡ ู‡ุจุฏุฃ ู…ุจุงุดุฑุฉ ููŠ chapter ูˆุงุญุฏ ุงู„ chapter
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ุงู„ุฃูˆู„ ุนูŠู†ูŠู‡ ู‡ูˆ chapter ุฑู‚ู… ุชู„ุงุชู‡ ุฅุฐุง ุงู„ course
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ุชุจุนู†ุง ุงุณู…ู‡ basic statistics ุฃูˆู„ chapter ุจู†ุณู…ูŠู‡
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numerical descriptive measures ุงู„ู„ูŠ ู‡ูŠ ู…ู‚ูŠูŠุณ
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ุงู„ูˆุตููŠุฉ ุงู„ุฑู‚ู…ูŠุฉุจุชุนุฑู ุงุญู†ุง ุงู„ data in general has
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two types ุงู…ุง numerical ู†ุณู…ูŠู‡ุง numerical data ุงูˆ
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ู†ุณู…ูŠู‡ุง ุงู„ุชุงู†ูŠุฉ categorical data ุงุฐุง ู†ุณู…ูŠู‡ุง
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numerical data ุงูˆ ุงุญู†ุง ู†ุณู…ูŠู‡ุง quantitative ุงูˆ
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ู†ุณู…ูŠู‡ุง qualitative
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ุงู„ุจูŠุงู†ุงุช ู„ุฏูŠู‡ุง ุฃุดุฎุงุต ู…ุฎุชู„ูุฉ ุจุดูƒู„ ุนุงู… ูˆุงุญุฏุฉ ุจู†ุณู…ูŠู‡ุง
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numerical data ุงูˆ quantitative data ูˆุงู„ุซุงู†ูŠุฉ
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ุจุณู…ูŠู‡ุง qualitative data ุงูˆ categorical data ุนู„ู‰
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ุณุจูŠู„ ุงู„ู…ุซุงู„ ุนู†ุฏู…ุง ู†ุชุญุฏุซ ุนู† ุนู…ุฑ ุนู…ุฑ ู‡ูˆ ุงู„ู†ู…ุฑูŠ ุงุฐุง
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ุนู…ุฑูƒ 18 ุณู†ุฉ 18 ู‡ูŠ ู‚ูŠู…ุฉ ู†ู…ุฑูŠ ุงุฐุง ูƒู†ุง ู†ุชุญุฏุซ ุนู† ุงู„ุถุบุท
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ุนู„ู‰ ุณุจูŠู„ ุงู„ู…ุซุงู„ุŒ ูƒู…ูŠุฉ ุนุงู…ุฉ ู‡ุฐู‡ ุงู„ุฏุฑุงุณุฉ ู‡ูˆ 70 ูƒูŠู„ูˆ
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ุฌุฑุงู…ุŒ ู‡ุฐุง ู‡ูˆ ุงู„ู‚ูŠู…ุฉ ุงู„ู†ู…ูˆุฐุฌูŠุฉ ุนู†ุฏู…ุง ู†ุชูƒู„ู… ุนู†
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ุงู„ุจูŠุงู†ุงุช ุงู„ูƒุชูˆุฑูŠูƒูŠุฉ ุฃูˆ ุงู„ุจูŠุงู†ุงุช ุงู„ุชู‚ู„ูŠุฏูŠุฉ ุนู„ู‰ ุณุจูŠู„
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ุงู„ู…ุซุงู„ ุงู„ุฌู†ุณ ุฅู…ุง ุงู„ู…ู„ุงูƒูŠู† ุฃูˆ ุงู„ู…ู„ุงูƒูŠู† ุฃูˆ ุงู„ู…ู„ุงูƒูŠู†
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ู‡ุฐุง
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ูŠุณู…ู‰ ุชู‚ู„ูŠุฏูŠุฉ ุชู‚ู„ูŠุฏูŠุฉ ู…ุนู†ุงู‡ ู†ูˆุนูŠ
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Quantitative ูŠุนู†ูŠ ุฑู‚ู…ูŠ This chapter focus on
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numerical descriptive measures ุจู†ุฑูƒุฒ ุนู„ู‰ ุงู„ู…ู‚ูŠูŠุณ
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ุงู„ูˆุตููŠุฉ ุงู„ุฑู‚ู…ูŠุฉ So we are talking about something
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like scores Now suppose your score is 90 90 is
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numerical valueุงู„ุงู† ูƒูŠู ู†ู‚ุฑุฑ ุงู„ู…ุนู„ูˆู…ุงุช ุฅุฐุง ูƒุงู†
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ู„ุฏูŠู†ุง ู‚ูŠู…ุฉ ู†ู…ูŠุฐูŠุฉุŸ ููŠ
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ู‡ุฐู‡ ุงู„ู‚ุตุฉ ู„ุฏูŠู†ุง ุฃุฑุจุน ุฃู‡ุฏุงู ุงู„ุฃูˆู„ุฉ
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ุชุณู…ุญ ุจู€Properties of Central Tendency ู„ุญุธุฉ ู„ุงู† ููŠ
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ุนู†ุฏูŠ ุฃูˆู„ ุชุนุฑูŠู Central Tendency ุฅูŠุด
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ู…ุนู†ู‰ CentralุŸู…ุฑูƒุฒ tendency ู†ุฒุนุฉ ุจุงู„ุธุจุท ูู‡ูŠ ุจูŠุณู…ูŠู‡ุง
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ู†ุฒุนุฉ ุงู„ู…ุฑูƒุฒูŠุฉ ุดูˆู ุงู†ุง ู‡ุญุงูˆู„ ุงู„ู…ุตุทู„ุญุงุช ุชุญูƒูŠ ุนุฑุจูŠ
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ุงู†ุฌู„ูŠุฒูŠ ูููŠ ุนู†ุฏูŠ describe the probabilities of
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central tendency ู…ุนู†ุงู‡ุง
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ุจุฏุฃ ุงุดุฑุญ ุงูˆ ุงูˆุตู ุฎุตุงุฆุต ู†ุฒุนุฉ ุงู„ู…ุฑูƒุฒูŠุฉ variation ุงูŠุด
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ูŠุนู†ูŠ variation
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variation ู…ุนู†ุงู‡ ุงุฎุชู„ุงู ุงูˆ
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ุชุดุชุช ุงูˆ ุชุจูŠู† and shape in numerical data ุดูƒู„
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ููŠ ู‡ุฐู‡ ุงู„ู…ู‚ุงู„ุฉ ุณู†ุชุญุฏุซ ุนู† ุซู„ุงุซ ุฃุณุฆู„ุฉ ุงู„ุฑุฆูŠุณูŠุฉ
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ู„ู„ู…ู‚ุงู„ุงุช ุงู„ุฑุณู…ูŠุฉ ุงู„ุฃูˆู„ู‰ ู‡ูŠ ุชู†ุฏู†ุณูŠุฉ ู…ุฑูƒุฒูŠุฉ ุงู„ุงุฎุชู„ุงู
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ุงูˆ ุชุดุชุทู ุงู„ุงุฎุชู„ุงู ุงูˆ ุชุดุชุทู ุงู„ุงุฎุชู„ุงู ุงูˆ ุชุดุชุทู
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ุงู„ุงุฎุชู„ุงู ุงูˆ ุชุดุชุทู ุงู„ุงุฎุชู„ุงู ุงูˆ ุชุดุชุทู ุงู„ุงุฎุชู„ุงู ุงูˆ
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ุชุดุชุทู ุงู„ุงุฎุชู„ุงู ุงูˆ ุชุดุชุทู ุงู„ุงุฎุชู„ุงู ุงูˆ ุชุดุชุทู ุงู„ุงุฎุชู„ุงู
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ุงูˆ ุชุดุชุทู ุงู„ุงุฎุชู„ุงู ุงูˆ ุชุดุชุทู ุงู„ุงุฎุชู„ุงู ุงูˆ ุชุดุชุทู
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ุงู„ุงุฎุชู„ุงู ุงูˆ
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ุชุดุชุทู ุงู„ุงุฎุชู„ุงู ุงูˆ ุชุดุชุทู ุงู„ุงุฎุชู„ุงู ุงูˆ ุชุดุชุทู ุงู„ุงุฎุชู„ุงู
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ุงูˆ ุชุดุชุท
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construct ู…ุนู†ุงู‡ุง ุจู†ุงุก
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ุฃูˆ ุฅู†ุดุงุก ุฃูˆ ุฅู†ุดุงุก ุฃูˆ ุฑุณู… ุณู…ูŠู‡ุง interpret ุชูุณูŠุฑ
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ุจุชูุณูŠุฑ ุจูƒุณ ุจู„ุงุช ุญุฏ ูŠุณู…ูŠู‡ุง ุจูƒุณ ุจู„ุงุช ู‡ู†ุงุฎุฏู‡ุง
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ุจุงู„ุชูุณูŠุฑ ุจุนุฏูŠู† ุฅุฐุง ุจู†ุนู…ู„ ุจู†ุงุก ูˆุงู„ุชุนู„ูŠู‚ ุฃูˆ ุงู„ุชูุณูŠุฑ
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ุจูƒุณ ุจู„ุงุช number three compute descriptive summary
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measures for a populationIn general, we have
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population suppose we are talking about IUG
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students ุจุชูƒู„ู… ุนู„ู‰ all IUG studentsุŒ ูƒู„ ุทู„ุจุฉ
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ุงู„ุฌุงู…ุนุฉ ุงู„ุฅุณู„ุงู…ูŠุฉ ุจุญูƒูŠ ูƒู„ุŒ ุจุชูƒู„ู… ุนู† population ุฅูŠุด
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ู…ุนู†ู‰ populationุŸ ู…ุฌุชู…ุนุŒ ู…ุฌุชู…ุน ูƒูƒู„ู„ูˆ ุฃุฎุฏุช ู…ู†ู‡ ุณุงู…ุจู„
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ุตุบูŠุฑู‡ ู‡ูƒุฐุง ู†ูุชุฑุถ ุณุงู…ุจู„ ู‡ูƒุฐุง ุทุจุนุง ุงู„ size ุชุจุน
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population ู…ู…ูƒู† ูŠูƒูˆู† ู…ุซู„ุง ุณุชุฉ ุนุดุฑ ุฃู„ูุŒ sixty
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thousand ุงู„ุณุงู…ุจู„ ุฅูŠุด ู‡ุชูƒูˆู†ุŸ ุฌุฒุกุŒ ู…ู…ูƒู† ูŠุงุฎุฏ ู…ูŠุฉ
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ู…ู†ู‡ู…ุŒ ุนูŠู†ุฉ number that he talks aboutHow can we
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compute descriptive measures for a population for
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the entire data for the entire data we have plus
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objective calculate the covariance and the
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coefficient of correlation variance ู…ุนู†ุงู‡ ุงูŠุดุŸ
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ุชุจุงู‡ู… ูˆ co .. ุงูŠ ุญุงุฌุฉ co ู…ุนู†ุงู‡ุง ู…ุดุชุฑูƒุฅุฐุง ุจุฏู†ุง ู†ุญุณุจ
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ุงู„ุชุจุงูŠู† ุงู„ู…ุดุชุฑูƒ ุฃูˆ ุณู…ูŠุญุงู†ุง ุงู„ุชุบูŠุฑ ู‡ุฐุง ููŠ ุขุฎุฑ
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ุงู„ุญู„ู‚ู‡ ุฅู† ุดุงุก ุงู„ู„ู‡ ุฅุฐุง ู†ุชูƒู„ู… ุนู† ุงู„ู€ covariance
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ุชุบูŠุฑ and
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the coefficient of correlation ุงู„ู„ูŠ ู‡ูˆ ุฃูŠุดุŸ ู…ุนุงู…ู„
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ุงู„ุฅุฑุชุจุงุท ู‡ุฐูˆู„ four objectives ู„ุญุธุฉ ููŠ ุนู†ุฏูŠ ุดูˆูŠุฉ
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ู…ุตุทู„ุญุงุช ุฌุฏูŠุฏุฉ ุฃู†ุง ุจุงู†ุตุญูƒ ุฎู„ู‘ูŠ ุนู†ุฏูƒ ุฏูุชุฑ ู„ุญุงู„ ูˆ ู‡ูŠูƒ
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ู„ู„ ..ู„ู„ู…ุตุทู„ุญุงุช ู‡ุฏูˆู„ ุฒูŠ Center Tendency Variation
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Shape Interpret Covariance Correlation ู‡ุฏูˆู„
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ู…ุตุทู„ุญุงุช ุฃู†ุง ุณุงุฎุฏูŠู†ู‡ุง ุจูƒุซุฑุฉ ูุจุงู„ุชุงู„ูŠ ูƒูˆูŠุณ ูŠูƒูˆู† ุนู†ุฏูƒ
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ุชู„ุฎูŠุต ู„ู‡ู… ุงู„ู„ูŠ
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ุฃู†ุง ู‡ุชูƒู„ู… ุนู„ู‰ summary definitions ุจุนุถ ุงู„ุชุนุฑูŠูุงุชูˆ
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ู‡ู†ุจุฏุฃ ุจุฃูˆู„ ูˆุงุญุฏ ุงู„ู€ central tendency ู…ุฑุฉ
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ุชุงู†ูŠุฉ ุงู„ central tendency ู…ุนู†ุงู‡ุง ู†ุฒุนุฉ ู…ุฑูƒุฒูŠุฉ
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ุงู„ู„ูŠ ู„ูˆ ุณุฃู„ุช ูƒู„ ูˆุงุญุฏุฉ ููŠูƒูˆุง ุนู…ุฑู‡ุงุŒ ู…ู…ูƒู† ูˆุงุญุฏุฉ
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ุงู„ุณุจุนุชุงุดุŒ ูˆุงุญุฏุฉ ุชู…ุงู†ุชุงุดุŒ ูˆุงุญุฏุฉ ุนุดุฑูŠู† ูˆู‡ุงูƒุฐุงุŒ ู„ูˆ
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ุนุงูŠุฒ ุฃุฎุฏ ุงู„ center ุชุจุนูƒู…ุŒ ู‡ุฐุง ุงู„ center ู…ุนู†ุงู‡
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ุงู„ู‚ูŠู… ุชูŠุฌูŠ ุญูˆุงู„ูŠู† ุจุนุถู‡ู…ุŒ ู…ุชูˆุณุทุงุชู‡ู…ุŒ ู ุงู„ center
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tendency is the extent to which the valuesุงู„ุนูŠู…ุง
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ุฏู‡ ุฃู†ู‡ ููŠ ุนู†ุฏู‡ ู‚ูŠู… of numerical variable group
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around a typical or central value ูŠุนู†ูŠ ุงู„ู‚ูŠู…
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ุชุชู…ุฑูƒุฒ ูˆูŠู†ุŸ ุงู„ู„ูŠ ู‡ูŠ ุงู„ู…ุชูˆุณุทุŒ ูˆุงุญุฏุฉ ู…ู†ู‡ุง ุงู„ู…ุชูˆุณุทุŒ
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ู‡ู†ุงุฎุฏู‡ุง ุจุนุฏ ุดูˆูŠุฉ ู„ุฐุง ุงู„ central ู…ุนู†ุงู‡ุง ุงู„ู‚ูŠู… ุชุชุฌู…ุน
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ุฃูˆ ุชุชู…ุฑูƒุฒ ุญูˆุงู„ูŠู† ู‚ูŠู…ุฉ ููŠ ุงู„ู†ุตูุŒ ุจู†ุณู…ูŠู‡ุง ุงู„ central
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value ุงู„ variation is the amount of dispersion
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ุงู†ุชุดุงุฑ ุฃูˆ ุชุดุชุชุŒ ู…ู‚ุฏุงุฑ ุงู„ุชุดุชุชor scattering away ู…ุด
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scattering away ุชู†ุชุดุฑ ุจุดูƒู„ ุจุนูŠุฏ ุนู† ุงู„ู€ central
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value ูŠุนู†ูŠ ุงู„ variation ุจู‚ูŠุณ ูƒู…ูŠุฉ ุงู„ุชุดุชุช ูŠุนู†ูŠ ุงุฐุง
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ุงู„ุชุดุชุช ุตุบูŠุฑ ูƒุจูŠุฑ ุงูˆ ู…ุชูˆุณุท that
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the values of a numerical variable shown ุงุฐุง ุงู„
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variation ุจู‚ูŠุณ ู…ู‚ุฏุงุฑ ุงู„ุชุดุชุช ู„ู„ู‚ูŠู… ุนู† ุงู„ู…ุชูˆุณุท
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ุงู„ุญุณุงุจูŠุทุจ ุงู„ shape ุงู„ุดูƒู„ is the pattern of the
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distribution pattern ู…ุนู†ุงู‡ ู†ู…ุท ุงู„ุชูˆุฒูŠุน of values
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from the lowest value to the largest ูŠุนู†ูŠ ุดูƒู„
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ุงู„ุชูˆุฒูŠุน ู…ู† ุฃุตุบุฑ ู‚ูŠู…ุฉ ู„ุฃูƒุจุฑ ู‚ูŠู…ุฉ ุจู†ุณู…ูŠู‡ the shape
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ุฅุฐุง ููŠ ุนู†ุฏ ุงู„ centralุงู„ู‚ูŠู… ู…ุฑูƒุฒูŠุฉ ุนู† ู‚ูŠู… ุนุงู…ุฉ ุฃูˆ
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ุจุนุถ ุงู„ุฃุญูŠุงู† ุงุณู…ู‡ุง ู‚ูŠู…ุฉ ู…ุฑูƒุฒูŠุฉ ู‡ุฐุง ุงุณู…ู‡ุง ุชู†ุฏู†ุณูŠุฉ
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ู…ุฑูƒุฒูŠุฉ ู…ุฎุชู„ูุฉ ู…ู‚ุฏุงุฑ ุงู„ุชุดุชุช ู…ู† ุงู„ู…ุฑูƒุฒ ูƒู… ุชุดุชุช ุนู„ู‰
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ุงู„ู…ุชูˆุณุท ุงู„ุญุณุงุจูŠ ุงู„ุชุงู„ุช ุงู„ุดูƒู„ ู‡ูˆ ุทุฑูŠู‚ุฉ ุงู„ู…ุดุงุฑูƒุฉ ู…ู†
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ุฃุตุบุฑ ุฅู„ู‰ ุฃูƒุจุฑ ู…ุง ู‡ูˆ ุฃุตุบุฑุŸุฃุตุบุฑ ุฃูƒุจุฑ ู‚ูŠู…ุฉ ู‡ุฐูˆู„ ุงู„ู€
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three definitions ู‡ู†ุงุฎุฏ ูƒู„ ูˆุงุญุฏ ุจุงู„ุชูุตูŠู„ The first
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one talks about measures of central tendency ู†ุงุฎุฏ
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ู…ู‚ูŠุงุณ ู„ู‡ู… ุฃูˆู„ ู…ู‚ูŠุงุณ is called the mean ูƒู„ู†ุง ุจู†ุนุฑู
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ุงู„ mean
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ุงู„ู€ mean ุนุจุงุฑุฉ ุนู† ุฅูŠุดุŸ ู…ุชูˆุณุท ุญุณุงุจูŠ it's called the
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arithmetic mean ุฃูˆ ู„ุณู‡ ูˆู„ุง ุจู†ุญูƒูŠ often just called
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the mean ุจุณ ุจุญูƒูŠ ุนู†ู‡ the mean it's
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the most common measure of central tendency ุฅูŠุด
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ูŠุนู†ูŠ most common central of central tendencyุŸุฃุดู‡ุฑ
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ู…ู‚ูŠุงุณ ุฃูˆ ุงู„ู…ู‚ูŠุงุณ ุงู„ุฃูƒุชุฑ ุดูŠูˆุนุง ุฃูˆ ุงู„ู…ู‚ูŠุงุณ ุงู„ุฃูƒุชุฑ
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ุงุณุชุฎุฏุงู…ุง ุฅุฐุง ุฃูƒุชุฑ ู…ู‚ูŠุงุณ ุณู†ุณุชุฎุฏู…ู‡ ุงู„ู€mean ุงู„ู€mean
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ู‡ูˆ ุฃูƒุชุฑ ู…ู‚ูŠุงุณ ุนุงู… ู„ู„ุชู†ุฏู†ุณูŠุฉ ุงู„ู…ุฑูƒุฒูŠุฉ ุงู„ุขู† ุงู„ุณุคุงู„
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ู‡ูˆ ูƒูŠู ู†ุณุชุฎุฏู… ุงู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ
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ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ
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ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ
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ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ูŠุงุณ ู„ู„ู…ู‚ุฃุญู†ุง ู†ุฃุฎุฐ
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ู…ุฌู…ูˆุนุฉ ู…ุฎุชู„ูุฉ ุฃูˆ ู…ุฌู…ูˆุนุฉ ุตูุฑ ู† ูŠุนู†ูŠ ุฃู†ู†ุง ู„ุฏูŠู†ุง ู†
143
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ุทู„ุงุจ ู† ู…ุซู„ุง ุฃูˆ ู…ู„ุงุญุธุงุช ู† ุฃูˆ ู…ุฌู…ูˆุนุฉ ู† ุงู„ู…ุฌู…ูˆุนุฉ
144
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ู…ุฎุชู„ูุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ
145
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ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ
146
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ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ
147
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ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ
148
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ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ ู…ู‚ุตุฏุฉ
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ู…ู‚ุตุฏุฉ ู…
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ู…ู…ูƒู† ุฃุณู…ูŠู‡ Y bar ู„ูƒู† ุบุงู„ุจุง ู†ุณุชุฎุฏู… X bar ุฅุฐุง X bar
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it stands for the mean or the arithmetic mean X
152
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bar equals .. we have a new symbol here this
153
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called summation summation
154
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ูŠุนู†ูŠ ู…ุฌู…ูˆุนุฉ summation
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of X I
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00:13:48,720 --> 00:13:53,940
ุงู„ู‚ูŠู…ุฉ ุฑู‚ู… I ูŠุนู†ูŠ ุงูŠุด ุงู„ู‚ูŠู…ุฉ ุฑู‚ู… IุŸ ุนู„ู‰ ุณุจูŠู„
157
00:13:53,940 --> 00:14:03,180
ุงู„ู…ุซุงู„ุŒ ุฅุฐุง ูƒุงู† ู„ุฏูŠู†ุง ู‡ุฐู‡ ุงู„ู‚ูŠู…ุฉ 16 20 26 30 40 50
158
00:14:03,180 --> 00:14:11,020
ูˆู…ุง ุฅู„ู‰ ุฐู„ูƒ ุงู„ุขู† ู‚ูŠู…ุฉ ุงู„ุฃูˆู„ู‰ 16ู†ุณุชุฎุฏู… X1 ู„ู€ 16 ูX1
159
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ู‡ูŠ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ
160
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ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„
161
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ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ
162
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ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„
163
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ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ
164
00:14:20,200 --> 00:14:21,880
ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„
165
00:14:21,880 --> 00:14:22,720
ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ
166
00:14:22,720 --> 00:14:34,500
ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃูˆู„
167
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ู‚ูŠู…ุฉ ุฃูˆู„ ู‚ูŠู…ุฉ ุฃ6ุŒ 1,2,3 ุฅู„ู‰ 6ุŒ ู„ุฐู„ูƒ ู†ุญู† ู„ุฏูŠู†ุง 6
168
00:14:41,090 --> 00:14:46,590
ู…ู„ุงุญุธุงุชุŒ ู„ุฐู„ูƒ ุตู…ู… ุงู„ู…ุฌู…ูˆุนุฉ ูŠู‚ู„ 6ุŒ ู„ุฐู„ูƒ ุตู…ู… XIุŒ I
169
00:14:46,590 --> 00:14:55,730
ูŠุชุฌู‡ ู…ู† 1 ุฅู„ู‰ 6ุŒ ูŠุนู†ูŠ X1 plus X2 ุฅู„ู‰ XNุŒ ุชู‚ู„ ู…ู† NุŒ
170
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ู…ุงู‡ูˆ NุŸ N ู‡ูˆ ุตู…ู… ุงู„ู…ุฌู…ูˆุนุฉSo the mean equals
171
00:15:06,290 --> 00:15:13,290
summation of XI divided by N Now once again X bar
172
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pronounced as X bar This symbol is called
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summation ู‡ุฐุง ู…ุณู…ู‰ ุงู„ู…ุฌู…ูˆุน ุงู„ Xุงุช ู‡ุฏูˆู„ ุนุจุงุฑุฉ ุนู† ุงู„
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observed values ุงู„ู‚ูŠู… ุงู„ู…ุดุงู‡ุฏุฉ ุงูŠุด ุงู„ observed
175
00:15:29,070 --> 00:15:34,670
ุงู„ู„ูŠ ู‡ูˆ ู…ุฏุฑุณุฉ 16 ู‡ู‚ูˆู„ observedobserved ูŠุนู†ูŠ
176
00:15:34,670 --> 00:15:40,230
ุงู„ู…ู„ุงุญุธุฉุŒ ุงู„ู‚ูŠู… ุงู„ู…ุดุงู‡ุฏุฉ ุฃูˆ ุงู„ู…ู„ุงุญุธุฉ ุฅู† ู‡ู…ุง ุนุดุฑูŠู†ุŒ
177
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ุณุชุฉ ูˆุนุดุฑูŠู†ุŒ ุชู„ุงุชูŠู† ูˆู…ุง ูƒุงู†ุŒ similar observed
178
00:15:42,150 --> 00:15:45,670
values ุฅุฐุง
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ู…ุนู†ุงู‡ ูƒุฏู‡ ุงู„ู€ the mean is the sum of the data ุฏูŠ
180
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ุจู‚ู‰ ูŠุชุจูŠู† ู…ุด ู‡ูŠูƒุŒ ู…ุชูˆุณุท ุนุจุงุฑุฉ ุนู† ุฅูŠุดุŸ ู…ุฌู…ูˆุน ุงู„ู‚ูŠู…
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ุนู„ู‰ ุฃุฏุชู‡ุงุŒ ูู‡ูŠ ุงู„ summation ุชุจุนู‡ู… ุนู„ู‰ ุฃุฏุชู‡ู…
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once again the most common measure of center
183
00:16:05,130 --> 00:16:09,670
tendency is the mean definition of the mean some
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00:16:09,670 --> 00:16:16,170
values divided by the number of values ู…ุฌู…ูˆุญู‡ู… ุนู„ู‰
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ุนุฏุฏู‡ู… number
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00:16:20,350 --> 00:16:23,470
three the mean is affected by extreme values or
187
00:16:23,470 --> 00:16:27,890
outliersู…ุด ู…ุนู†ุงู‡ affected by extreme values ุจุชุฃุซุฑ
188
00:16:27,890 --> 00:16:33,850
extreme ู…ุนู†ุงู‡ุงู‚ูŠู… ุดุงุฏุฉ ุงูˆ ู…ุชุทุฑูุฉ ู‚ูŠู… ุดุงุฏุฉ ุงูˆ
189
00:16:33,850 --> 00:16:38,950
ู…ุชุทุฑูุฉ ู…ุนู†ุงู‡ุง ุงู…ุง large ุงูˆ small ุงุฐุง ุงู„ mean is
190
00:16:38,950 --> 00:16:46,410
affected by extreme values now
191
00:16:46,410 --> 00:16:51,110
let's see how can we compute the mean now suppose
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00:16:51,110 --> 00:17:00,350
we have this data set we have 11 12 13 14 and 15
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00:17:06,180 --> 00:17:10,100
ุงู„ุงู† ู„ูƒูŠ ู†ุญุตู„ ุนู„ู‰ ู…ุฌู…ูˆุญ ุงู„ู€ X bar ู†ุถูŠู ูู‚ุท ู‡ุฐู‡
194
00:17:10,100 --> 00:17:14,580
ุงู„ู‚ูŠู… ุซู…
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00:17:14,580 --> 00:17:20,500
ู†ู‚ู„ ุจุงู„ N ู…ุฌู…ูˆุญู‡ู… ูˆู…ุฌุณู… ุนู„ู‰ ุนุฏุฏู‡ู… 11 13 ู„ุบุงูŠุฉ ู…ุง
196
00:17:20,500 --> 00:17:26,640
ุฎู„ุต ู„ูˆ ุฌู…ุนุชู‡ู… ุจุทู„ุน 65 over 5 so 13 ูู…ุฌู…ูˆุนู‡ู… ุนู„ู‰
197
00:17:26,640 --> 00:17:34,160
ุนุฏุฏู‡ู… 13 ูู…ุฌู…ูˆุญู‡ู…
198
00:17:34,160 --> 00:17:43,610
ุนู„ู‰ ุนุฏุฏู‡ู…ุงู„ุฃู† ู†ูุชุฑุถ ุงู„ุทุงู„ุจ ุงู„ู„ูŠ ุฌุงุจ 15 ุดูŠู„ู†ุงู‡ ูˆ
199
00:17:43,610 --> 00:17:53,770
ูŠู‚ูˆู… ุจุฅุนุงุฏุฉ 15 value ูˆ ูŠู‚ูˆู… ุจุฅุนุงุฏุฉ 20 now let's
200
00:17:53,770 --> 00:17:58,410
calculate the new mean the new mean is just 11 12
201
00:17:58,410 --> 00:18:03,690
13 plus 20 over 5 this gives 14
202
00:18:07,100 --> 00:18:14,140
ุงู„ู‚ูŠู…ุฉ ูƒุงู†ุช 13 ูˆุนู†ุฏ ุชุบูŠูŠุฑู‡ุง ุฅู„ู‰ 20 ุชุบูŠุฑ ุงู„ู‚ูŠู…ุฉ ุฅู„ู‰
203
00:18:14,140 --> 00:18:19,280
14 ูˆู‡ุฐุง ูŠุนู†ูŠ ุฃู† ุงู„ู‚ูŠู…ุฉ ุชุชุฃุซุฑ ู…ู† ู‡ุฐุง ุงู„ู‚ูŠู…ุฉ ุงู„ู€ 20
204
00:18:19,280 --> 00:18:26,460
ุจุนูŠุฏุฉ ู‚ู„ูŠู„ ู…ู† 15 ุชุนุชุจุฑ ู‚ูŠู…ุฉ ุฃูƒุชุฑูŠู… ุชู„ุงุญุธ ุฃู† ุงู„ู‚ูŠู…ุฉ
205
00:18:26,460 --> 00:18:31,960
ุชุชุบูŠุฑ ุตุญ ุชุชุบูŠุฑ ุจู…ู‚ุฏุงุฑ ุจุณูŠุท ูˆู„ูƒู† ุชุชุบูŠุฑุฅุฐุง ุงู„ุณุจุจ
206
00:18:31,960 --> 00:18:35,060
ุจุชุบูŠุฑ ู„ุฃู† ุงู„ู€mean ุชุนูŠุด ุชุนุฑูŠูู‡ sum of values
207
00:18:35,060 --> 00:18:39,440
divided by n ูู„ู…ุง ุบูŠุฑู‡ุง 15 ุจ20 ุฃูƒูŠุฏ ุงู„ู€mean ู‡ูŠุชุบูŠุฑ
208
00:18:39,440 --> 00:18:49,320
ุฅุฐุง ุงู„ู€mean is affected by extreme values one
209
00:18:49,320 --> 00:18:55,900
more example suppose we have this data one up to
210
00:18:55,900 --> 00:18:56,880
nine
211
00:19:00,190 --> 00:19:07,470
ุงู„ุงู† ู…ุงุฐุง ูŠุนู†ูŠ ู‡ุฐุง ุงู„ุจูŠุงู†ุงุชุŸ ุณู…ูŠุฉ ุชู‚ุฑูŠุจุง ู…ู† N ุฅุฐุง
212
00:19:07,470 --> 00:19:11,650
ู‚ู…ู†ุง ู†ู‚ู„ ู‡ุฐู‡ ุงู„ู‚ูŠู… ู…ู†
213
00:19:11,650 --> 00:19:16,850
ูˆุงุญุฏุฉ ุฅู„ู‰ ุชุณุนุฉ ู…ุฌู…ูˆุญู‡ู… ุฎู…ุณุฉ ูˆุงุฑุจุนูŠู†ุŒ forty five
214
00:19:16,850 --> 00:19:26,770
ุนุฏุฏู‡ู… ุชุณุนุฉ ูู‚ูŠู…ู‡ุง ุฎู…ุณุฉ ุงุฐุง ู‚ู…ู†ุง ู†ุถูŠู ู…ุงุฆุฉ ุฅู„ู‰ ู‡ุฐู‡
215
00:19:26,770 --> 00:19:27,050
ุงู„ู‚ูŠู…
216
00:19:30,040 --> 00:19:34,200
100 ู‡ูŠ ู‚ูŠู…ุฉ ุฃูƒุชุฑุŒ ู‚ูŠู…ุฉ ูƒุจูŠุฑุฉุŒ outlierุŒ ู‚ูŠู…ุฉ ุดุงุฏุฉ
217
00:19:34,200 --> 00:19:40,540
ู„ูˆ ุถูุช ุงู„ู…ูŠุฉ ุนู„ูŠู‡ู…ุŒ ุงู„ู€ new mean ู…ุด ู‡ูŠุณุงูˆูŠุŒ ุตุงุฑ
218
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145ุŒ ุงู„ู€ sample size ู‡ูˆ 10 ู„ุฃู†ู†ุง ู‚ู…ู†ุง ุจุฅุถุงูุฉ ู‚ูŠู…ุฉ
219
00:19:45,700 --> 00:19:51,180
ูˆุงุญุฏุฉุŒ 14.5 ู„ุญุธุฉุŒ
220
00:19:51,180 --> 00:19:55,080
ุงู„ู‚ูŠู…ุฉ ุงู„ู‚ุฏูŠู…ุฉ ูƒุงู†ุช 5ุŒ ูˆ ุงู„ุขู† ุชุตุจุญ 14.5 ู‡ุฐุง ูŠุนู†ูŠ
221
00:19:55,080 --> 00:20:00,300
ุฃู† ุงู„ู‚ูŠู…ุฉ ุชุชุฃุซุฑ ู…ู† ู‡ุฐุง ุงู„ู‚ูŠู…ุฉ ุงู„ุฃูƒุชุฑูˆุงุถุญ ุฃู†ู‡ ูŠุชุฃุซุฑ
222
00:20:00,300 --> 00:20:04,820
ุงู„ู‚ูŠู… ุงู„ูƒุจูŠุฑุฉ ุชู„ุงุญุธ ุงู„ู‚ูŠู…ุฉ ูƒุงู†ุช ุฎู…ุณุฉ ุตุงุฑุช ุฃุฑุจุนุชุงุดุฑ
223
00:20:04,820 --> 00:20:08,480
ูˆ ู†ุต ุชู‚ุฑูŠุจุง ุชู„ุงุชุฉ ุถุนู ุนุดุงู† ูƒุฏู‡ ุจู†ุญูƒูŠ the mean is
224
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affected by extreme value ุฅุฐุง ุจุชุฃุซุฑ ุงู„ู‚ูŠู… ุงู„ุดุฏู‘ุฉ
225
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ู‡ูŠ
226
00:20:16,500 --> 00:20:20,580
ูŠุนู†ูŠ ู„ุฅู† ุจู‚ุฏุฑุด ุฃุฌูŠุจ ุนู„ูŠู‡ุง ุงู„ุณุคุงู„ ู‡ู†ุฎู„ูŠู‡ ู„ุจุนุฏูŠ ู„ู…ุง
227
00:20:20,580 --> 00:20:25,500
ู†ุงุฎุฏ ุญุงุฌุฉ ุงุณู…ู‡ุง ุงู„ box plot ู„ูƒู† ู…ุจุฏุฃูŠุง ุงู„ twenty
228
00:20:25,500 --> 00:20:31,620
ูŠุนู†ูŠ ุงู„ู„ูŠ ุชู„ุงุญุธูŠุงู„ู€ 13 ู„ 14 ุงู„ูุฑู‚ ู…ุด ูƒุจูŠุฑ ุนุดุงู† ูƒุฏู‡
229
00:20:31,620 --> 00:20:37,040
ุงู„ 20 ู…ู…ูƒู† ู…ุด extreme value ู„ูƒู† ู„ู…ุง ุญุงุทู„ุช ุงู„ู…ูŠุฉ ู…ู†
230
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5 ู„ 14 ูˆ ู†ุต ูˆุงุถุญ ุงู„ู…ุณุงูุฉ ูƒุจูŠุฑุฉ ุจูŠู†ู‡ู… ู„ูƒู† ู…ู‚ุฏุฑุด
231
00:20:42,360 --> 00:20:46,840
ุงุญุฏุฏ ุงู„ุขู† ู„ูƒู† ูˆุงุถุญ ุงู†ู‡ ููŠ ุงู„ data ุงู„ุฃูˆู„ู‰ ุงู„ 20 is
232
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not that extreme value ู…ุด ูƒุชูŠุฑุฉ ุจุนูŠุฏุฉ ุนุดุงู† ูƒุฏู‡ ุงู„
233
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mean ูƒุงู† 13 ุตุงุฑ 14 ุงู„ูุฑู‚ ู…ุด ูƒุจูŠุฑุณุคุงู„ูƒ ูƒูˆูŠุณ ุจุณ ุฃุฌุงุจ
234
00:20:56,740 --> 00:21:01,940
ุนู„ูŠู‡ ุฅู† ุดุงุก ุงู„ู„ู‡ ุฎู„ุงู„ ุงู„ู„ู‚ุงุกุงุช ุงู„ู„ูŠ ุฌุงูŠุฉ the
235
00:21:01,940 --> 00:21:07,740
next measure is called the median ุงูŠุด medianุŸ ูˆุณูŠุท
236
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ุงู„ median ู…ุนู†ุงู‡ ุงู„ูˆุณูŠุท ุชุนุฑู
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ุงู„ูˆุณูŠุท the value in the middle ุงู„ู‚ูŠู…ุฉ ุงู„ู ูˆ ุงู„ู†ุตุจุณ
238
00:21:17,480 --> 00:21:20,520
after we arrange the data from smallest to largest
239
00:21:20,520 --> 00:21:23,500
ู„ู…ุง ุฃุฑุชุจ ุงู„ู‚ูŠุงู… ูŠุนู†ูŠ ุฅุฐุง ูƒุงู† ุนู†ุฏูƒ ุดูˆูŠุฉ ู‚ูŠู…
240
00:21:23,500 --> 00:21:27,280
ุจุชุฑุชุจูŠู‡ู… ู…ู† ุงู„ุตุบูŠุฑ ู„ู„ูƒุจูŠุฑ ุฃูˆ ุงู„ุนูƒุณ ุงู„ู‚ูŠู… ุงู„ู„ูŠ ููŠ
241
00:21:27,280 --> 00:21:30,360
ุงู„ูˆุณุท ู‡ูŠ ุนุจุงุฑุฉ ุนู† ุงู„ media ู…ุนู†ุงู‡ ู‚ูŠู…ุฉ ููŠ ุงู„ูˆุณุท
242
00:21:30,360 --> 00:21:33,140
ูŠุนู†ูŠ ุงู„ู„ูŠ ุนู„ู‰ ุงู„ูŠู…ูŠู† ุจุชุณุงูˆูŠ ุงู„ู„ูŠ ุนู„ู‰ ุงู„ุดู…ุงู„ ูŠุนู†ูŠ
243
00:21:33,140 --> 00:21:36,280
ุนุฏุฏ ุงู„ู‚ูŠุงู… ุงู„ู„ูŠ ุนู„ู‰ ุงู„ูŠุณุงุฑ ุจุชุณุงูˆูŠ ุนุฏุฏ ุงู„ู‚ูŠุงู… ุงู„ู„ูŠ
244
00:21:36,280 --> 00:21:40,460
ุนู„ู‰ ุงู„ูŠู…ูŠู† ู‡ุฐุง ู…ุนู†ุงู‡ in an ordered array ููŠ ู…ุตููˆูุฉ
245
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ู…ุฑุชุจุฉ the median is the middle numbermiddle number
246
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ุงู„ู‚ูŠู…ุฉ ุฅูŠุดุŸ ููŠ ุงู„ู…ู†ุชุตู ู…ุนู†ู‰ ุงู„ู‚ูŠู…ุฉ ููŠ ุงู„ู…ู†ุชุตู ูŠุนู†ูŠ
247
00:21:52,490 --> 00:21:59,010
ุฎู…ุณูŠู† ููŠ ุงู„ู…ูŠุฉ above ูˆ ุฎู…ุณูŠู† ููŠ ุงู„ู…ูŠุฉ below ู„ุฃู†
248
00:21:59,010 --> 00:22:02,970
ูˆูŠู† ุงู„ูˆุณุทุฉ ููŠ ุฃุตุงุจุนูƒุŸ ููŠ ุงู„ู†ุต ู…ุธุจูˆุท ุฅูŠุด ู…ุนู†ู‰ ููŠ
249
00:22:02,970 --> 00:22:05,850
ุงู„ู†ุตุŸ ูŠุนู†ูŠ ุงุชู†ูŠู† ุนู„ู‰ ุงู„ุดู…ุงู„ ูˆ ุงุชู†ูŠู† ุนู„ู‰ ุงู„ูŠู…ูŠู† ููŠ
250
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ุงู„ middle and the value in the middle when we
251
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arrange the data from smallest to largest ุฃูˆ ู…ู†
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largest to smallestุฃุฑุจุนุฉ ู‡ูˆ ู†ูุณ ุงู„ูƒู„ุจ ุงู„ุตุบูŠุฑ ุฃูŠู‡ุง
253
00:22:15,190 --> 00:22:21,090
ุจุชุญูƒูŠ .. ู„ูˆ ูƒุงู† ุฃุนุฏุงุฏู‡ู… ุฃุฑุจุนุฉ ู‡ุฌูŠุจูƒ ุฃุณูˆุฃ ุจุนุฏ ุงู„
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slide ู‡ุฐูŠ ุงู„ู„ูŠ ู‡ู… ู†ุญูƒูŠ ุนู„ู‰ ุงู„ุดุบู„ ุงู„ุทุจูŠุนูŠ ู„ูˆ ูƒุงู†
255
00:22:25,710 --> 00:22:27,990
ู‡ุฐุง ุดูˆูŠุฉ ู‚ูŠู… ุงู„ medium ุงู„ู‚ูŠู…ุฉ ุงู„ู„ูŠ ููŠ ุงู„ู†ุต ุจุนุฏ
256
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ู…ุฑุชุจู‡ู… ูˆุนู„ู‰ ูŠู…ูŠู†ู‡ู… ุจุณูˆุก ุนู„ู‰ ุดู…ุงู„ู‡ู… ุฎู„ูŠู†ุง ู†ุดูˆูู‡ุง
257
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ุจุนุฏ ุดูˆูŠุฉ ู…ุง ู†ุณุชุนุฌู„ุด ูŠุนู†ูŠ ุฌุงูˆุจ ุน ุณุคุงู„ูƒ ุจุนุฏ ุดูˆูŠุฉ
258
00:22:35,730 --> 00:22:39,710
ุชุทู„ุน ุนู„ู‰ ุงู„ู‚ูŠู… ู‡ุฐูˆู„ ู†ูุณ ุงู„ู‚ูŠู… ุงู„ู„ูŠ ูุงุชุช11 .. 12 ..
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13 .. 14 .. 15 .. The median and the value in the
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middle ูˆ ู‡ุฏูˆู„ ูˆุงุถุญ ุฃู†ู‡ we arrange the data ู…ุฑุชุจูŠู†
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ุงู„ value in the middle ู‡ูŠ
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ุงู„ median ู„ุญุธุฉ
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13 ู‡ุฐู‡ุงู„ู‚ูŠู…ุฉ 13 ู‡ูŠ ุงู„ู‚ูŠู…ุฉ ุงู„ู…ุชูˆุณุทุฉ ู„ุฃู† ู‡ู†ุงูƒ
264
00:23:01,880 --> 00:23:06,060
ุงุชุตุงู„ูŠู† ุชุญุช 13 ูˆ ุงุชุตุงู„ูŠู† ููˆู‚ู‡ุง ุงุชุตุงู„ูŠู† ุงู‚ู„ ูˆ
265
00:23:06,060 --> 00:23:11,960
ุงุชุตุงู„ูŠู† ุงุนู„ู‰ ู„ุฐู„ูƒ 13 ู‡ูŠ ุงู„ู‚ูŠู…ุฉ ุงู„ู…ุชูˆุณุทุฉ ู„ุญุธุฉ
266
00:23:11,960 --> 00:23:14,440
ุงู„ู‚ูŠู…ุฉ ุงู„ู…ุชูˆุณุทุฉ ูƒุงู†ุช ุชู„ุงุชูŠู† ุจุฑุถู‡ ุงู„ู‚ูŠู…ุฉ ุงู„ู…ุชูˆุณุทุฉ
267
00:23:14,440 --> 00:23:15,400
ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ
268
00:23:15,400 --> 00:23:18,240
ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ
269
00:23:18,240 --> 00:23:18,700
ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ
270
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ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ ุชู„ุงุชุฉ
271
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ุงู„ู‚ูŠู…ุฉ ุงู„ู€ Famous ู…ุง ุงุชุฃุซุฑุด ุจุงู„ู€ Extreme Value
272
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ู…ุธุจูˆุทุŸ ู‡ู†ุงูƒ ูƒุงู†ุช 14 ุชุฃุซุฑ ุงู„ู€ MedianุŒ ุงู„ู€ Main ู„ูƒู†
273
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ูˆุงุถุญ ุฅู† ุงู„ู€ Median is not affected by largest
274
00:23:37,970 --> 00:23:41,630
value ูŠุนู†ูŠ ุงู„ุฎู…ุณุฉ ุนุดุฑ ูŠุนู†ูŠ ู„ูˆ ุฃู†ุง ุบู…ุถุช ุนู„ูŠู‡ุง ูˆ
275
00:23:41,630 --> 00:23:48,210
ุญุงุทูŠุช ุจุฏู„ู‡ุง 200 ุจุงู„ุชุงู… ุงู„ Median ูƒุฏู‡ุŸ 13 ู…ุน ูƒุฏู‡ ุงู„
276
00:23:48,210 --> 00:23:52,470
outliers ู…ุงู„ุงุด ู‚ูŠู…ุฉ ู‡ู†ุง ูŠุนู†ูŠ ุงู„ Median is not
277
00:23:52,470 --> 00:23:58,790
affectedby extreme outliers or outliers as the
278
00:23:58,790 --> 00:24:04,910
mean ุฅุฐุง ุงู„ู€ median is less sensitive ุฃู‚ู„ ุญุณุงุณูŠุฉ
279
00:24:04,910 --> 00:24:09,710
than the median to extreme values ู…ุน ูƒุฏู‡ outlier
280
00:24:09,710 --> 00:24:15,810
affect the mean much more than the median ุงู„
281
00:24:15,810 --> 00:24:19,790
outlier ุจุชุฃุซุฑ ุนู„ู‰ ุงู„ mean ุฃูƒุชุฑ ู…ู†ู‡ุง ุนู„ู‰ ุงู„ median
282
00:24:19,790 --> 00:24:24,770
ุฅุฐุง ุงู„ outliers ุจุชุฃุซุฑ ุนู„ู‰ ุงู„ mean ุฃูƒุชุฑุนุงู„ู€ mean
283
00:24:24,770 --> 00:24:31,790
ุงู„ู€ mean ุงู„ู„ูŠ ูุงุช ู„ุญุธุฉ ูƒุงู† 13 ุตุงุฑ 14 ู‡ู†ุง
284
00:24:31,790 --> 00:24:36,250
ุงู„ median ู…ุง ุฒุงู„ the same value ูŠุนู†ูŠ ุจุนุฏ ูƒุฏู‡ if we
285
00:24:36,250 --> 00:24:39,830
replace the largest value by any other value
286
00:24:39,830 --> 00:24:43,150
larger than that one then the median stay the same
287
00:24:43,150 --> 00:24:47,870
ุจุชุฃุซุฑุด ูˆู„ูˆ ุงุชุฃุซุฑ ุชุฃุซุฑู‡ ู…ุด ูƒุจูŠุฑ ุชุทู„ุน ุงู„ example
288
00:24:47,870 --> 00:24:51,570
ุงู„ู„ูŠ ูุงุช ู…ู† 1 ุฅู„ู‰ 9 ุญูƒูŠู†ุง ุงู„ mean was 5
289
00:24:53,820 --> 00:25:01,200
ูˆู„ู…ู‘ุง ุถูู†ุง ุงู„ู…ูŠุฉ ุตุงุฑ ุงู„ mean 14.5 ุทุจ ุทู„ุน ุงู„ median
290
00:25:01,200 --> 00:25:08,100
ููŠ ุงู„ุญู„ู‚ุฉ ุงู„ุฃูˆู„ู‰ ุงูˆ ุงู„ median ู…ุงุชุฃุซุฑุด ู‡ูŠ ููŠ ุงู„ู†ุต
291
00:25:08,100 --> 00:25:14,560
ู…ุธุจูˆุท ููˆุงุถุญ ุงู„ mean ูˆ ุงู„ median ู…ุง ู„ู‡ู… ุฒูŠ ุจุนุถ ุฅู„ู‰
292
00:25:14,560 --> 00:25:20,000
ู„ู…ุง ุถูุช ุงู„ู…ูŠุฉ ู„ุญุธุฉ ู„ู…ุง ุถูุช ุงู„ู…ูŠุฉ ุนู„ูŠู‡ู…
293
00:25:23,150 --> 00:25:27,930
ุจุทู„ุช ุงู„ุฎู…ุณุฉ ุงู„ median ู„ุฃู†
294
00:25:27,930 --> 00:25:35,130
ุงู„ุฎู…ุณุฉ ุนู„ู‰ ูŠุณุงุฑู‡ุง four values ูˆุนู„ู‰ ู…ูŠู†ู‡ุง ุฎู…ุณุฉ ู‡ุฐุง
295
00:25:35,130 --> 00:25:39,350
ูƒุงู† ุชุณุงูˆูŠ ุฒู…ูŠู†ูƒ ูˆู„ูŠุด ู…ูŠุงู‡ุŒ ุทุจ ูˆุงู„ุณุชุฉุŸ ุจุฑุถู‡ ุงู„ุณุชุฉ
296
00:25:39,350 --> 00:25:42,590
ู…ุด the median ู„ุฃู†ู‡ ุนู„ู‰ ูŠุณุงุฑู‡ุง ุฎู…ุณุฉ ูˆุนู„ู‰ ู…ูŠู†ู‡ุง
297
00:25:42,590 --> 00:25:49,550
ุฃุฑุจุนุฉ ุฅุฐุง ุงู„ median ุนุจุงุฑุฉ ุนู† ุฃูŠุดุŸ ุงู„ average ู„ู„
298
00:25:49,550 --> 00:25:54,890
middle pointsุงู„ู€ average ู„ ู‡ุฏูˆู„ ุงุชู†ูŠู† ูุงู„ average
299
00:25:54,890 --> 00:26:02,510
ุชู…ุญู‡ู… ุฎู…ุณุฉ ุฒูŠ ุณุชุฉ ุนู„ู‰ ุงุชู†ูŠู† ุฎู…ุณุฉ ูˆ ู†ุตู ุงุฐุง ู„ู…ุง
300
00:26:02,510 --> 00:26:08,910
ุงูƒูˆู† ุนู†ุฏู‰ ู‡ุฏูˆู„ุฉ ูƒู… ูˆุงุญุฏุฉ ุงุนุฏุฏู‡ู… ุนุดุฑุฉ ู…ุด ู‡ูŠูƒ ู„ู…ุง
301
00:26:08,910 --> 00:26:15,510
ูŠูƒูˆู† even ูŠุนู†ูŠ ุนุฏุฏ ุฒูˆุฌูŠ ุจุชุงุฎุฏ ุงู„ average ู„ู„ two
302
00:26:15,510 --> 00:26:19,470
middle points five plus six ุนู„ู‰ ุงุชู†ูŠู† ู„ุญุธุฉ ุงู„
303
00:26:19,470 --> 00:26:20,690
median ูƒุงู† ุฎู…ุณุฉ
304
00:26:23,680 --> 00:26:28,400
ู„ู…ุง ุถูุช ุนู„ูŠู‡ ุงู„ู…ูŠุฉ ุตุงุฑ ุฌุฏูŠู‡ุด ุฎู…ุณุฉ ูˆ ู†ุต ุงุชุบูŠุฑุช
305
00:26:28,400 --> 00:26:34,460
ู‚ูŠู…ุชู‡ ู…ู† ุฎู…ุณุฉ ู„ุฎู…ุณุฉ ูˆ ู†ุต ุงุฐุง ุงู„ mean ูƒุงู† ุฎู…ุณุฉ ุตุงุฑุช
306
00:26:34,460 --> 00:26:42,140
ุงุฑุจุนุฉ ุนุดุฑ ูˆ ู†ุต ู„ูƒู† ุงู„ median ูƒุงู†ุช ุฎู…ุณุฉ ุตุงุฑุช ุฎู…ุณุฉ ูˆ
307
00:26:42,140 --> 00:26:46,340
ู†ุต ุงู„ู…ุนู†ู‰ ูƒุฏู‡ ู…ูŠู† ุงู„ less sensitive ุงู„ mean ูˆู„ุง ุงู„
308
00:26:46,340 --> 00:26:51,050
medianุงู„ู€ median ุฃู‚ู„ ุญุณุงุณูŠุฉ ู‡ูˆ ุงุชุบูŠุฑ ู…ู† ุฎู…ุณุฉ ุตุญูŠุญ
309
00:26:51,050 --> 00:26:55,210
ู„ุฎู…ุณุฉ ูˆ ู†ุต ุจุณ ุงู„ุชุบูŠุฑ ุชุจู‚ู‰ ุฃู‚ู„ ู…ู† ุชุบูŠุฑ ุงู„ mean ุงู„
310
00:26:55,210 --> 00:26:59,150
mean ู…ู† ุฎู…ุณุฉ ู„ุงุฑุจุนุชุงุด ูˆ ู†ุต ูˆุงุถุญ ุงู† ุงู„ mean ุชุนุชุจุฑ
311
00:26:59,150 --> 00:27:07,450
extreme value ุฅุฐุง in general the median is less
312
00:27:07,450 --> 00:27:10,130
sensitive than the mean to extreme value ุฃู‚ู„
313
00:27:10,130 --> 00:27:10,750
ุญุณุงุณูŠุฉ
314
00:27:19,270 --> 00:27:24,230
ุงู„ุณlide ุงู„ุชุงู„ู ูŠุชูƒู„ู… ุนู† ู…ูˆู‚ุน ุงู„ medium ูƒูŠู ูŠู…ูƒู†ู†ุง
315
00:27:24,230 --> 00:27:28,990
ุชุญุตูŠู„ ู…ูˆู‚ุน ุงู„ mediumุŸ ูŠุนู†ูŠ ูƒูŠู ู…ู…ูƒู† ู†ุนู…ู„ ุงู„ู…ูƒุงู†
316
00:27:28,990 --> 00:27:36,890
ุชุจุน ุงู„ mediumุŸ ู‡ู†ุงูƒ ุงุซู†ูŠู† ุญุงู„ุงุช ุฅุฐุง N ุบุฑูŠุจ N
317
00:27:36,890 --> 00:27:43,450
ุฅูŠุด ุบุฑูŠุจุŸ ุบุฑูŠุจ ู…ุนู†ุงู‡ ุนุฏุฏ ูุฑุฏูŠ ูุฑุฏูŠ ูŠุนู†ูŠ ุชู„ุงุชุฉุŒ
318
00:27:43,450 --> 00:27:48,040
ุฎู…ุณุฉุŒ ุณุจุนุฉุŒ ุชุณุนุฉ ูˆ ู‡ูƒุฐุงููŠ ุงู„ุญุงู„ุฉ ุงู„ู€ location of
319
00:27:48,040 --> 00:27:51,260
the median when the values are in numerical order
320
00:27:51,260 --> 00:27:55,380
it means from smallest to largest the median
321
00:27:55,380 --> 00:28:02,720
position is n plus one over two ู‡ูŠ ุงู„ position so
322
00:28:02,720 --> 00:28:11,880
n plus one over two for this example n was five so
323
00:28:11,880 --> 00:28:13,180
the position of the median
324
00:28:16,120 --> 00:28:22,520
equal five plus one over two three ุฅุฐุง ุงู„ู…ูƒุงู† ุชุจุน
325
00:28:22,520 --> 00:28:27,440
ุฑู‚ู… ุชู„ุงุชุฉ ุจุนุฏ ู…ุฑุชุจ ู„ุญุธุฉ ู‡ุฐุง ุงู„ first position
326
00:28:27,440 --> 00:28:33,720
ุงู„ุดูŠุฎ ู‡ุฐุง ุฃูˆู„ ู…ูƒุงู† ูˆู‡ุฐุง ุงู„ุชุงู†ูŠ ูˆู‡ุฐุง ุงู„ุชุงู„ุช ูˆู‡ุฐุง
327
00:28:33,720 --> 00:28:38,320
ุงู„ุฑุงุจุน ูˆุงู„ุฎุงู…ุณ ุงู„ medium is in the third position
328
00:28:38,320 --> 00:28:41,200
ุงู„ third position ู…ูˆู‚ุน ุงู„ุชุงู„ุช ุงู„ู„ูŠ ู‡ูˆ ุงู„ุชู„ุงุชุฉ ุนุดุฑ
329
00:28:41,200 --> 00:28:43,820
ู„ุญุธุฉ ุงู„ุชู„ุงุชุฉ is not the medium
330
00:28:47,860 --> 00:28:52,540
is not the median ู‡ุฐุง ุนุจุงุฑุฉ ุนู† ุงู„ู…ูˆุถูˆุน ุชุจุนู‡
331
00:28:52,540 --> 00:28:55,720
position of the median ุงูŠุด ุจูŠุทู„ุน ุฏุงูŠู…ุง ูุฑุฏ ุงู‡ ู„ูˆ
332
00:28:55,720 --> 00:29:01,040
ูƒุงู† ู‡ุฐุง ุงู„ุณุช ุน ุงุชู†ูŠู† ูุฑุฏูŠ ู„ูˆ ุชุณุนุฉ ุชุณุนุฉ ุฒูŠ ูˆุงุญุฏ
333
00:29:01,040 --> 00:29:07,940
ุงุชู†ูŠู† ูุฑุฏูŠ ูˆูƒุฐุง ุทุจ ุงู„ู…ุซู„ุฉ ุนุฏุฏู‡ู… ุฌุฏูŠุด ุชุณุนุฉ ุชุณุนุฉ ุฒูŠ
334
00:29:07,940 --> 00:29:12,630
ูˆุงุญุฏ ุงุชู†ูŠู† ุฎู…ุณุฉ ุงู„ู…ูƒุงู† ุฑู‚ู… ุฎู…ุณุฉู‡ู†ุง ุทู„ุน ุฎู…ุณุฉ
335
00:29:12,630 --> 00:29:16,930
ุจุงู„ุตุฏูุฉ ู…ุด ุจุงู„ุถุฑูˆุฑุฉ ูŠุทู„ุน ุฎู…ุณุฉ ู‡ูˆ ุฎู…ุณุฉ ู„ุญุธุฉ ู‡ู†ุง ุทู„ุน
336
00:29:16,930 --> 00:29:22,630
ุงู„ุชุงู„ุช ุชู„ุชุงุดุฑ ู…ุด ุจุงู„ุถุฑูˆุฑุฉ ุฅุฐุง ุงู„ medium position n
337
00:29:22,630 --> 00:29:27,710
plus one over two if the number of values is odd
338
00:29:27,710 --> 00:29:31,650
ุฅุฐุง ุนุฏุฏู‡ู… ูุฑุฏูŠ the median is the middle number
339
00:29:31,650 --> 00:29:38,770
ุงู„ู‚ุจู„ ููŠ ุงู„ู†ุต if the number is even ุฅุฐุง ูƒุงู† ุฒูˆุฌูŠ
340
00:29:38,770 --> 00:29:42,950
ุฒูŠ ู‡ูŠูƒ ู„ู…ุง ุถูู†ุง ุงู„ู…ูŠุฉ ุชูˆุฅุฐุง ูƒุงู†ุช ุงู„ู…ู‚ุงู„ุฉ ู…ุฑุชุจุทุฉุŒ
341
00:29:42,950 --> 00:29:45,970
ูุฅู† ู…ู‚ุงู„ุฉ ุงู„ู€ Median ู‡ูŠ ุนุงู…ู„ุฉ ุงู„ุงุซู†ูŠู† ุงู„ู…ู‚ุงู„ูŠู† ุฃูˆ
342
00:29:45,970 --> 00:29:49,430
ุงู„ุงุซู†ูŠู† ุงู„ู…ู‚ุงู„ูŠูŠู† ู„ุญุธุฉุŒ ู‡ู†ุง ุฃุฎุฐู†ุง ุนุงู…ู„ุฉ ุงู„ุงุซู†ูŠู†
343
00:29:49,430 --> 00:29:55,850
ุงู„ู…ู‚ุงู„ูŠูŠู† ู„ู€ 5 6 2 ูˆุงุจู‚ู‰ ููŠ ุฐูƒุฑ ุงู† N ุจู„ุณ 1 2 ู„ูŠุณ
344
00:29:55,850 --> 00:30:01,450
ู…ู‚ุงู„ุฉ ุงู„ู…ู‚ุงู„ุฉ ูู‚ุท
345
00:30:01,450 --> 00:30:06,570
ู…ู‚ุงู„ุฉ ุงู„ู…ู‚ุงู„ุฉ ููŠ ุญุงู„ุฉ ุนุงู…ู„ุฉ ุฅุฐุง ุงู„ู…ูƒุงู† ุชุจุนู‡ N ุจู„ุณ
346
00:30:06,570 --> 00:30:09,450
1 2 ูŠุนู†ูŠ ู„ูˆ ูƒุงู† ู…ุฎุชุงุฑ ู…ุฑุชุจุท ุญูƒูŠู†ุง ุฅูŠุด ุงู„ position
347
00:30:11,720 --> 00:30:16,720
ุชุจุนู‡ ุงู„ู€ equation ุนุจุงุฑุฉ ุนู† n plus one over two ู‡ุฐุง
348
00:30:16,720 --> 00:30:21,460
ู„ูˆ ูƒุงู†ุช n is odd ุฅุฐุง ูƒุงู† even ุจู†ุงุฎุฏ ุงู„ู€ middle ุงู„
349
00:30:21,460 --> 00:30:25,000
average ู„ two middle points ุทุจุนุง ุงู„ two middle
350
00:30:25,000 --> 00:30:37,620
points ุงู„ู„ูŠ ุทู„ุน ุนู„ูŠู‡ู… ู‡ู†ุง suppose
351
00:30:37,620 --> 00:30:42,820
we have this dataุงู„ุงู† even ุงูˆ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
352
00:30:42,820 --> 00:30:44,880
ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
353
00:30:44,880 --> 00:30:45,380
ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
354
00:30:45,380 --> 00:30:51,420
ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
355
00:30:51,420 --> 00:30:53,600
ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
356
00:30:53,600 --> 00:30:53,700
ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
357
00:30:53,700 --> 00:30:53,740
ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
358
00:30:53,740 --> 00:30:54,860
ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
359
00:30:54,860 --> 00:30:56,060
ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
360
00:30:56,060 --> 00:30:59,120
ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
361
00:30:59,120 --> 00:31:05,200
ุบูŠุฑ ุบูŠุฑ ุบูŠุฑ
362
00:31:05,200 --> 00:31:08,360
ุบูŠุฑ ุบ
363
00:31:11,670 --> 00:31:20,710
ู‚ูŠู…ุฉ ุงู„ู€ x3 ุนุจุงุฑุฉ ุนู† 9 ูˆุงู„ุชุงู†ูŠุฉ ุนุจุงุฑุฉ ุนู† 2 9 plus
364
00:31:20,710 --> 00:31:28,530
12 ุนุจุงุฑุฉ ุนู† 2 21 ูŠุนู†ูŠ 10.5 ุฒูŠ ุงู„ medium 10.5 ุทูŠุจ x
365
00:31:28,530 --> 00:31:33,170
ุชู„ุงุชุฉ ู‡ุฐู‡ ุนุจุงุฑุฉ ุนู† ู…ูˆุฌุฉ ุงู„ุชุงู„ุช x4 ู…ูˆุฌุฉ ุงู„ุฑุงุจุน ูƒูŠู
366
00:31:33,170 --> 00:31:41,950
ุทู„ุนู†ุง ุงู„ุชู„ุงุชุฉ ุงู„ุงู† 6 ู…ุธุจูˆุท ูุงู† ุน 2ุจุชู‚ุนุฏ ุงูƒุณ ุณุชุฉ ุน
367
00:31:41,950 --> 00:31:45,410
ุงุชู†ูŠู† ุงู„ุชู„ุงุชุฉ ูˆ ุงู„ู„ูŠ ุจุนุฏู‡ ุงู„ู„ูŠ ุจุนุฏู‡ ุงู„ู„ูŠ ู‡ูˆ ุงูƒุณ
368
00:31:45,410 --> 00:31:49,290
ุงุฑุจุนุฉ ุงู„ู„ูŠ ู‡ูˆ ุนุจุงุฑุฉ ุนู† ู…ูŠู† ุงูƒุณ ุงู† ุน ุงุชู†ูŠู† ูˆ ุฒุงุฆุฏ
369
00:31:49,290 --> 00:31:54,150
ูˆุงุญุฏ ูู„ู…ุง ุจูƒูˆู† ุนู†ุฏู‰ even number ุงู„ position ุจูƒูˆู†
370
00:31:54,150 --> 00:31:58,690
ุงู† ุน ุงุชู†ูŠู† ูˆ ุงู„ู„ูŠ ุจุนุฏู‡ ุงู† ุน ุงุชู†ูŠู† in the next
371
00:31:58,690 --> 00:32:06,110
number ูŠุนู†ูŠ ู„ูˆ ู…ุซู„ุฉ ุฒูŠ ู‡ูŠูƒ ู…ู† ูˆุงุญุฏ ู„ุบุงูŠุฉ ู…ูŠุฉ ูŠุนู†ูŠ
372
00:32:06,110 --> 00:32:09,610
ุงู† ุจุงู„ุณุจุน ุนุดุฑ ู…ุด ู‡ูŠูƒุงู„ู€ median ุนุจุงุฑุฉ ุนู† ุฅูŠุด ุงู„
373
00:32:09,610 --> 00:32:16,510
position ุชุจุนู‡ู… N ุน 2 ูˆ ุงู„ู„ูŠ ุจุนุฏู‡ ู…ูŠู† N ุน 2ุŸ ู‡ุงูŠ N
374
00:32:16,510 --> 00:32:23,350
ุน 2 ุนุดุฑุฉ ุน ุงุชู†ูŠู† ุฎู…ุณุฉ ูˆ ุงู„ู„ูŠ ุจุนุฏู‡ ุงู„ุณุงุฏุณุฉ ุฎู…ุณุฉ ูˆ
375
00:32:23,350 --> 00:32:32,080
ุงู„ุณุงุฏุณุฉ ุฎู„ุงุตุŸ ุฅุฐุง the mean is the averageุงู„ู…ุนู†ู‰ ู‡ูŠ
376
00:32:32,080 --> 00:32:36,220
ุนุฏุฏ ุงู„ู…ู‚ุงูˆู…ุงุช ุงู„ู…ู‚ุงูˆู…ุฉ ุจุงู„ู€ N ุงู„ู…ู‚ุงูˆู…ุฉ ู‡ูŠ ุงู„ู‚ูŠู…ุฉ
377
00:32:36,220 --> 00:32:38,980
ููŠ ุงู„ู…ู‚ุงูˆู…ุฉ ุจุนุฏ ุฃู†ู†ุง ู‚ู…ู†ุง ุจุชุฌู‡ูŠุฒ ุงู„ุจูŠุงู†ุงุช ู…ู† ุฃูƒุชุฑ
378
00:32:38,980 --> 00:32:44,920
ุฅู„ู‰ ุฃูƒุชุฑ ุฃูˆ ุฃูƒุชุฑ ุฅู„ู‰ ุฃูƒุชุฑ ุฅุฐุง ูƒุงู†ุช N ุบูŠุฑ ู…ุญุฏูˆุฏุฉุŒ
379
00:32:44,920 --> 00:32:48,980
ูู…ู‚ุงูˆู…ุฉ ุงู„ู…ู‚ุงูˆู…ุฉ ู‡ูŠ N plus one over two ุฅู„ุง ุฅุฐุง
380
00:32:48,980 --> 00:32:52,080
ูƒุงู†ุช N ู…ุฑุชุจุทุฉุŒ ูู…ู‚ุงูˆู…ุฉ ุงู„ู€ N ู‡ูŠ ุนุฏุฏ ุงู„ู…ู‚ุงูˆู…ุฉ ุจูŠู†
381
00:32:52,080 --> 00:32:54,420
ุงู„ุงุซู†ูŠู† ู…ู‚ุงูˆู…ุฉ ุงู„ู…ู‚ุงูˆู…ุฉ ุจูŠู† ุงู„ุงุซู†ูŠู† ู…ู‚ุงูˆู…ุฉ
382
00:32:54,420 --> 00:33:03,830
ุงู„ู…ู‚ุงูˆู…ุฉ ููŠ ุงู„ู…ูˆู‚ุนxn2 ูˆุงู„ุชุงู„ูŠ xn2 plus 1 ู…ุซู„ู‹ุง ู…ุฑุฉ
383
00:33:03,830 --> 00:33:10,390
ุฃุฎุฑู‰ุŒ ูุฅู† ุงู„ู€ n ู‡ูˆ 20ุŒ ูู…ุงุฐุง
384
00:33:10,390 --> 00:33:15,070
ู‡ูŠ ุงู„ู…ู‚ุงูˆู…ุฉ ุงู„ู…ุชูˆุณุทุฉุŸ
385
00:33:15,070 --> 00:33:22,730
ุงู„ู€ n 20 ูŠุนู†ูŠ ุฃู† ู‡ู†ุงูƒ ู…ู‚ุงูˆู…ุฉ ู…ุฎุชู„ูุฉ ุงู„ู„ูŠ ู‡ูˆ ู…ูŠู†ุŸ n
386
00:33:22,730 --> 00:33:27,650
ุนู„ู‰ 2 ูˆ ุงู„ู„ูŠ ุจุนุฏู‡N ุน 2 ูŠุนู†ูŠ ุนุดุฑุฉ ูˆ ุงู„ู„ูŠ ุจุนุฏู‡ 11
387
00:33:27,650 --> 00:33:31,990
ุฅุฐุง ุงู„ positions ู„ู„ median ุนุดุฑุฉ ูˆ 11 ุจูŠุงุฎุฏ ุงู„
388
00:33:31,990 --> 00:33:35,650
average ุชุจุน ุงู„ values ูˆ ุจุฌุณู… ุน 2 ูˆ ูˆู‚ุช ุฌุณู… ุน 10 ูˆ
389
00:33:35,650 --> 00:33:42,010
11 ุน 2 ู‡ุฏูˆู„ ุงู„ู…ูƒุงู† ุงู„ location ุฎู„ุงุต ุทุจ ู„ูˆ ูƒุงู† N
390
00:33:42,010 --> 00:33:52,650
ุจุชุณุงูˆูŠ 21 N odd ุงู„ู…ูƒุงู† ุงู„ู„ูŠ N ุฒูŠ 1 ุน 2 ุงู„ู…ูƒุงู† ุฑู‚ู…
391
00:33:52,650 --> 00:33:59,680
11 ู‡ุฐุง ุฎู„ูŠ ุจุงู„ูƒis the position of the media ุงูŠู‡ ุฏู‡
392
00:33:59,680 --> 00:34:08,760
position ุงูŠู‡ ุฏู‡ ู‡ูŠูƒ position ุงู„ู…ูƒุงู† ุงู„ุตุจุงุต
393
00:34:08,760 --> 00:34:12,020
ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰
394
00:34:12,020 --> 00:34:14,060
ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰
395
00:34:14,060 --> 00:34:20,940
ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰ ุจูŠุจู‚ู‰
396
00:34:20,940 --> 00:34:23,860
ุจูŠุจ
397
00:34:26,580 --> 00:34:32,760
ุฎู…ุณ ุฒูŠ ูˆุงุญุฏ ุงุชู†ูŠู† ุชู„ุงุชุฉ ุชุฑุชูŠู† ุงู„ูƒู„ุงู… ุฏู‡ ู…ุด ุตุญ ู„ูŠุด
398
00:34:32,760 --> 00:34:38,560
ู„ุงุฒู… ู†ุฑุชุจู‡ู… ุงู„ุฃูˆู„ ุงุญู†ุง ุญูƒูŠู†ุง ู‡ุงูŠ ุงู„ุชุนุฑูŠู ุฏู‡
399
00:34:38,560 --> 00:34:44,260
ุงู„ุชุนุฑูŠู ุงู„ median in
400
00:34:44,260 --> 00:34:49,080
an ordered array ููŠ ุงู„ู…ุตูˆูุฉ ุงู„ู…ุฑุชุจุฉ the median is
401
00:34:49,080 --> 00:34:52,360
the middle number ุฅุฐุง ุจู‚ู‰ ุฃู†ุง ูƒุฏู‡ ู„ุงุฒู…ุด ุฃุนู…ู„ ููŠ
402
00:34:52,360 --> 00:34:55,680
ุงู„ุฃูˆู„ ุฃุฑุชุจู‡ู… ููŠ ุงู„ุฃูˆู„ ู‡ูŠ thirteen ุงู„ุฃูˆู„
403
00:35:03,200 --> 00:35:07,920
ุงู„ู…ูƒุงู† ุงู„ุชุงู„ุช 16 ู…ุด 13 ูŠู„ุงุฒู… ููŠ ุงู„ุฃูˆู„ we have to
404
00:35:07,920 --> 00:35:11,100
arrange the data from smallest to largest ุงูˆ
405
00:35:11,100 --> 00:35:15,680
largest to smallest ู„ุญุธุฉ ู„ูˆ ุฑุชุจุชู… ุจุงู„ุนูƒุณ ุนุดุฑูŠู†
406
00:35:15,680 --> 00:35:20,260
ุชุณุนุฉ ุนุดุฑ ุณุชุฉ ุนุดุฑ ุจุฑุถู‡ the median and the value in
407
00:35:20,260 --> 00:35:25,480
the middle we have the same value any question
408
00:35:28,460 --> 00:35:34,720
ุงู„ู†ู‡ุงุฑ ูŠุชูƒู„ู… ุนู† ุซุงู„ุซ ู…ูŠุฌุงุฑ ู„ู„ุชู†ุฏู†ุณูŠุฉ ุงู„ู…ุฑูƒุฒูŠุฉ ุญุชู‰
409
00:35:34,720 --> 00:35:39,000
ุงู„ุขู† ุชูƒู„ู…ู†ุง ุนู† ุงุชู†ูŠู† ู…ูŠุฌุงุฑูŠู† ู…ูŠู† ูˆู…ูŠุฏูŠุงู† ุซุงู„ุซ
410
00:35:39,000 --> 00:35:44,880
ู…ูŠุฌุงุฑ ูŠุณู…ู‰ ุงู„ mood ุงู„ mood ูŠุนู†ูŠ ู…ู† ุฃูŠู†ุŸ ู‡ูˆ ููŠ ู†ู…ุท
411
00:35:44,880 --> 00:35:50,480
ู„ูƒู† ููŠ ู„ุญุธุฉ ู…ุนู†ุงู‡ ู…ู† ุฃูŠู†ุŸ
412
00:35:50,480 --> 00:35:54,940
ุฅุฐุง
413
00:35:54,940 --> 00:35:55,960
ุญูƒูŠู†ุง ุนู„ู‰ ุงู„ mean
414
00:35:59,170 --> 00:36:05,950
ุญูƒูŠู†ุง ุนู„ู‰ ุงู„ู€ median number three mode ุงู„ู…ู†ูˆุงู„
415
00:36:05,950 --> 00:36:16,090
ุงู„ู…ู†ูˆุงู„ ุชุนุฑูŠูู‡ value that you care most often ูŠุนู†ูŠ
416
00:36:16,090 --> 00:36:19,730
ุงู„ู‚ูŠู…ุฉ ุงู„ู„ูŠ ุจุชุชูƒุฑุฑ ุฃูƒุชุฑ ุดูŠุก ุงู„ู‚ูŠู…ุฉ ุงู„ุฃูƒุชุฑ ุชูƒุฑุงุฑ
417
00:36:19,730 --> 00:36:27,210
not affected by extreme valuesุจุชุฃุซุฑุด ุฒูŠ ุงู„ mean ูˆ
418
00:36:27,210 --> 00:36:30,470
ุงู„ median ุงู„ mean ุจุชุฃุซุฑ ุงู„ median ุจุชุฃุซุฑ ุจุณ ุฃู‚ู„
419
00:36:30,470 --> 00:36:34,130
ุงู„ุชุฃุซูŠุฑ ู…ู† ุงู„ median ุจุณ ู‡ุฐุง not affected by
420
00:36:34,130 --> 00:36:39,370
extreme values ุจุชุฃุซุฑุด ุงู„ mean ูˆ ุงู„ median are used
421
00:36:39,370 --> 00:36:43,190
only for numerical data ู„ู„ุจูŠุงู†ุงุช ุงู„ุฑู‚ู…ูŠุฉ ุฒูŠ ุงู„ age
422
00:36:43,190 --> 00:36:50,410
ุงู„ weight ุงู„ score ูˆ ู‡ูƒุฐุง ุงู„ mode is used for
423
00:36:50,410 --> 00:36:54,140
either numerical or categorical dataูŠุง ุจู†ูุน
424
00:36:54,140 --> 00:36:57,660
ุงุณุชุฎุฏู…ู‡ ู„ู„ุฑู‚ู… ูˆุงู„ูˆุตู ุฒูŠ ุงู„ู€ gender ุงู„ู„ูŠ ุญูƒูŠู†ุง ุนู„ูŠู‡
425
00:36:57,660 --> 00:37:02,520
ููŠ ุงู„ุฃูˆู„ ุฅุฐุง ุงู„ู…ูŠุฒุฉ ุงู„ุฌูŠุฏุฉ ู„ู„ู…ูˆุฏ ุงู†ู‡ ูŠุณุชุฎุฏู… .. not
426
00:37:02,520 --> 00:37:06,160
affected by outliers or extreme values and can be
427
00:37:06,160 --> 00:37:12,120
used for both numerical and categorical data there
428
00:37:12,120 --> 00:37:16,440
are maybe sometimes there may be no .. no mood
429
00:37:16,440 --> 00:37:20,260
ู…ู…ูƒู† ู…ุงููŠุด mood ู…ุด ุฏู‡ ู…ุด ุถุฑูˆุฑูŠ ูŠูƒูˆู† ููŠู‡ mood ุงูˆ
430
00:37:20,260 --> 00:37:25,290
ูˆูŠู† ูˆุฌุฏ it could be uniqueูŠุนู†ูŠ ูˆุงุญุฏ ุฃูˆ ููŠ ุจุนุถ
431
00:37:25,290 --> 00:37:31,050
ุงู„ุฃุญูŠุงู† ู…ู…ูƒู† ูŠูƒูˆู† ุนู†ุฏูƒ ุฃูƒุชุฑ ู…ู† ู…ูˆุถูˆุน ุงุฐุง ุงู„ู…ูˆุถูˆุน
432
00:37:31,050 --> 00:37:39,110
ุฃูƒุชุฑ ู…ุณุชู…ุฑ ุฃูˆ ุฃูƒุชุฑ ุญุฏูˆุซ ู‚ูŠู…ุฉ ุงู„ุฃูƒุชุฑ ุธู‡ูˆุฑุง ุฃูˆ ุฃูƒุชุฑ
433
00:37:39,110 --> 00:37:43,310
ุชูƒุฑุงุฑุง ุฃูˆ ุฃูƒุชุฑ ุญุฏูˆุซุง ู„ูˆ ุทู„ุนุช ุน ุงู„ data ุงู„ู„ูŠ ู‡ู†ุง
434
00:37:43,310 --> 00:37:47,450
ู†ุญู†
435
00:37:47,450 --> 00:37:53,140
ู„ุง ู„ุฏูŠู†ุง ู†ู‚ุทุฉ ูˆุงุญุฏุฉ ุฃูƒุชุฑ ู…ุฑุฉ3 ู…ุฑุฉุŒ 5 ู…ุฑุฉ ู…ุฑุชูŠู†ุŒ 8
436
00:37:53,140 --> 00:37:57,440
ู…ุฑุฉ ู…ุฑุชูŠู†ุŒ 10 ู…ุฑุฉ ู…ุฑุชูŠู†ุŒ 12 ู…ุฑุฉ ู…ุฑุชูŠู†ุŒ 13 ู…ุฑุฉ
437
00:37:57,440 --> 00:38:02,280
ู…ุฑุชูŠู† ูˆ14 ู…ุฑุฉ ู…ุฑุชูŠู† ุงู„ุฃู† ู…ุงู‡ูŠ ุฃูƒุชุฑ ู‚ูŠู…ุฉ ู…ุนู„ูˆู…ุฉ
438
00:38:02,280 --> 00:38:04,320
ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ
439
00:38:04,320 --> 00:38:07,320
ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ
440
00:38:07,320 --> 00:38:07,460
ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ
441
00:38:07,460 --> 00:38:08,520
ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ
442
00:38:08,520 --> 00:38:18,560
ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…ุฉ ู…ุนู„ูˆู…
443
00:38:20,330 --> 00:38:30,930
ู…ุซู„ ู‡ุฐุง ุงู„ู…ุซุงู„ ู‡ู†ุง ู†ุญู† ู„ุฏูŠู†ุง 1 3 4 2 5 3 9 10 12
444
00:38:30,930 --> 00:38:39,470
12 13 ูˆ 14 9 ู…ู…ูƒู† 3 ู…ุฑุงุช ูุงู„ุญุจ 9 ูููŠ ู‡ุฐู‡ ุงู„ุญุงู„ุฉ
445
00:38:39,470 --> 00:38:48,350
ูู‡ู†ุงูƒ ูู‚ุท ุญุจ ูˆุงุญุฏ ูุงู„ุญุจ 9 ู„ู„ู…ุซุงู„
446
00:38:48,350 --> 00:38:57,790
ุงู„ุขุฎุฑู†ุญู† ู„ุฏูŠู†ุง 0ุŒ 1ุŒ 2ุŒ 3ุŒ 5 ูˆ6 ููŠ ู‡ุฐู‡ ุงู„ุญุงู„ุฉ ูƒู„
447
00:38:57,790 --> 00:39:03,330
ู‚ูŠู…ุฉ ุชุญุฏุซ ู…ุฑุฉ ูˆุงุญุฏุฉ ู‡ุฐุง ูŠุนู†ูŠ ููŠ ู‡ุฐู‡ ุงู„ุญุงู„ุฉ ู„ูŠุณ
448
00:39:03,330 --> 00:39:12,370
ู‡ู†ุงูƒ ู…ูˆุถูˆุน ุทุจ ู„ูˆ ุฒูˆุฏุช ูˆุงุญุฏุฉ ู‡ู†ุง
449
00:39:12,370 --> 00:39:15,550
ู…ุน
450
00:39:15,550 --> 00:39:21,620
ูƒุฏู‡ two modes ุงู„ู„ูŠ ู‡ูˆ ุงู„ุฎู…ุณุฉ ูˆุงู„ุชุณุนุฉfive ูˆ nine ุทุจ
451
00:39:21,620 --> 00:39:27,060
ู„ูˆ ุฌูŠุช ู‡ู†ุง ุฒูˆุฏุช ูˆุงุญุฏุฉ ู„ู„ุณุชุฉ ุจุตูŠุฑ ุงู„ุณุชุฉ ู‡ูŠ ุงู„ mode
452
00:39:27,060 --> 00:39:33,740
ู…ุตุจูˆุฑุŸ ู„ุฃู† ุงู„ุณุชุฉ ู‡ูŠ ุงู„ุฃูƒุชุฑ ุชูƒุฑุงุฑ ู…ุฑุชูŠู† ุทุจ ู„ูˆ ูƒุฑุฑุช
453
00:39:33,740 --> 00:39:40,800
ู‡ูŠูƒ ุตุงุฑ ุงู„ุฃุชู†ูŠู† ูˆุงู„ุชู„ุงุชุฉ ูˆุงู„ุณุชุฉ ู‡ู…ุง ุงู„ modes ุฅุฐุง
454
00:39:40,800 --> 00:39:45,280
ู…ู…ูƒู† ูŠูƒูˆู† there is only one mode or sometimes the
455
00:39:45,280 --> 00:39:48,340
mode does not exist ุฃูˆ there are
456
00:39:51,720 --> 00:39:57,480
ู…ู…ูƒู† ูŠูƒูˆู† ู…ูˆุฌูˆุฏ ุงูˆ ุบูŠุฑ ู…ูˆุฌูˆุฏ ู…ู…ูƒู†
457
00:39:57,480 --> 00:40:02,000
ูŠูƒูˆู† ู…ูˆุฌูˆุฏ ุงูˆ ุบูŠุฑ ู…ูˆุฌูˆุฏ ู…ู…ูƒู† ูŠูƒูˆู† ู…ูˆุฌูˆุฏ ุงูˆ ุบูŠุฑ
458
00:40:02,000 --> 00:40:06,440
ู…ูˆุฌูˆุฏ ุฏุนูˆู†ุง
459
00:40:06,440 --> 00:40:08,860
ู†ู„ู‚ูŠ ู†ุธุฑุฉ ุนู„ู‰ ู‡ุฐุง ุงู„ู…ุซุงู„ ุฏุนูˆู†ุง ู†ู„ู‚ูŠ ู†ุธุฑุฉ ุนู„ู‰ ู‡ุฐุง
460
00:40:08,860 --> 00:40:09,360
ุงู„ู…ุซุงู„ ุฏุนูˆู†ุง ู†ู„ู‚ูŠ ู†ุธุฑุฉ ุนู„ู‰ ู‡ุฐุง ุงู„ู…ุซู„ ุฏุนูˆู†ุง ู†ู„ู‚ูŠ
461
00:40:09,360 --> 00:40:09,640
ู†ุธุฑุฉ ุนู„ู‰ ู‡ุฐุง ุงู„ู…ุซู„ ุฏุนูˆู†ุง ู†ู„ู‚ูŠ ู†ุธุฑุฉ ุนู„ู‰ ู‡ุฐุง ุงู„ู…ุซู„
462
00:40:09,640 --> 00:40:12,700
ุฏุนูˆู†ุง ู†ู„ู‚ูŠ ู†ุธุฑุฉ ุนู„ู‰ ู‡ุฐุง ุงู„ู…ุซู„ ุฏุนูˆู†ุง ู†ู„ู‚ูŠ ู†ุธุฑุฉ ุนู„ู‰
463
00:40:12,700 --> 00:40:12,760
ู‡ุฐุง ุงู„ู…ุซู„ ุฏุนูˆู†ุง ู†ู„ู‚ูŠ ู†ุธุฑุฉ ุนู„ู‰ ู‡ุฐุง ุงู„ู…ุซู„ ุฏุนูˆู†ุง ู†ู„ู‚ูŠ
464
00:40:12,760 --> 00:40:13,400
ู†ุธุฑุฉ ุนู„ู‰ ู‡ุฐุง ุงู„ู…ุซู„ ุฏุนูˆู†ุง ู†ู„ู‚ูŠ ู†ุธุฑุฉ ุนู„ู‰ ู‡ุฐุง ุงู„ู…ุซู„
465
00:40:13,400 --> 00:40:15,800
ุฏุนูˆู†ุง ู†ู„ู‚ูŠ ู†ุธุฑุฉ ุนู„ู‰ ู‡ุฐุง ุงู„ู…ุซู„ ุฏุนูˆู†ุง ู†ู„ู‚ูŠ ู†ุธุฑุฉ ุนู„ู‰
466
00:40:15,800 --> 00:40:19,640
ู‡ุฐุง ุงู„ู…ุซู„ ุฏุน
467
00:40:19,720 --> 00:40:25,640
100 ูˆ100 ูˆุฏุนูˆู†ุง ู†ุฑู‰ ูƒูŠู ู†ุณุชุฎุฏู… ุงู„ุงู†ุชุฌุงุฑ ุงู„ุงู†ุชุฌุงุฑ
468
00:40:25,640 --> 00:40:29,020
ุงู„ุงู†ุชุฌุงุฑ
469
00:40:29,020 --> 00:40:35,600
ู‡ูˆ ุงุถุงูุฉ ู‡ุฐู‡ ุงู„ู‚ูŠู… ุซู… ู†ู‚ู„ ู…ู† ุนุฏุฏ ุงู„ู…ู†ุฒู„ ุงู„ุงู†ุชุฌุงุฑ
470
00:40:35,600 --> 00:40:44,320
ุชุจุนู‡ู… ุนู„ู‰ ุฃุฏุฏู‡ู… ูˆุงุถุญ ู…ุฌู…ูˆุญู‡ู… 3 ู…ู„ูŠูˆู† ู†ู‚ู„ ู…ู† 5 ูŠุนู†ูŠ
471
00:40:44,320 --> 00:40:51,320
600000 ุฅุฐุง ุงู„ุงู†ุชุฌุงุฑ ุชุจุนู‡ู… 600000ุงู„ู…ูŠุฏูŠุงู† ูŠุฌุจ ุฃู†
472
00:40:51,320 --> 00:40:53,820
ู†ุฎู„ู‚ู‡ ู…ู† ุฃูƒุจุฑ ุฅู„ู‰ ุฃูƒุจุฑ ุฃูˆ ุฃูƒุจุฑ ุฅู„ู‰ ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ
473
00:40:53,820 --> 00:40:56,540
ุฅู„ู‰ ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ
474
00:40:56,540 --> 00:40:57,880
ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู†
475
00:40:57,880 --> 00:40:59,820
ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู†
476
00:40:59,820 --> 00:41:03,880
ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู†
477
00:41:03,880 --> 00:41:06,180
ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู†
478
00:41:06,180 --> 00:41:06,500
ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู†
479
00:41:06,500 --> 00:41:16,000
ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒุจุฑ ู…ู† ุฃูƒ
480
00:41:17,180 --> 00:41:20,660
ุงู„ู€ mean ู„ุฃู†ู‡ ุฃุฎุฐ ูƒู„ ุงู„ู€ values ูุชุฃุซุฑ ุจุงู„ู€ mean
481
00:41:20,660 --> 00:41:24,700
ุจุงู„ู€ extreme ุจุงู„ู€ 200 ุฃู„ู ูˆ ุจุงู„ู€ 2 ู…ู„ูŠูˆู† ูˆ ุชุฃุซุฑ
482
00:41:24,700 --> 00:41:27,980
ุจุงู„ู€ 100 ุฃู„ู ุงู„ู„ูŠ ุชุญุช ู„ุฃู†ู‡ ุชุนุชุจุฑ 100 ุจุนูŠุฏุฉ ุนู† ุงู„ู€
483
00:41:27,980 --> 00:41:30,400
2 ู…ู„ูŠูˆู† ูˆ ุงู„ู€ 2 ู…ู„ูŠูˆู† ุจุนูŠุฏุฉ ุนู† ุงู„ูƒู„ ุจุงู„ุชุงู„ูŠ ู‡ูˆ
484
00:41:30,400 --> 00:41:35,620
ุชุฃุซุฑ ุจุงู„ู€ 2 ู…ู„ูŠูˆู† ุฃูƒุชุฑ ูุงู„ู€ median ุทู„ุน 300 ุฃู„ู ุทุจ
485
00:41:35,620 --> 00:41:39,160
ุงู„ู…ูˆุถ is the most frequent value ุงู„ู‚ูŠู…ุฉ ุงู„ุฃูƒุซุฑ
486
00:41:39,160 --> 00:41:43,880
ุชูƒุฑุงุฑ ุฃูƒุชุฑ ูˆุงุญุฏุฉ ูƒุฑุฑุฉ 100 ุฃู„ู ู„ุญุธุฉ ุฃู† ุงู„ุขู† three
487
00:41:43,880 --> 00:41:47,760
different measures for center tendencymain,
488
00:41:48,060 --> 00:41:54,300
median, mode ุงู„ุงู† ุงู„ุณุคุงู„ ู‡ูˆ ุงูŠู‡ ุงู„ู…ู‚ูŠุงุณ ุงู„ู„ูŠ ู„ุงุฒู…
489
00:41:54,300 --> 00:41:59,320
ุงุณุชุฎุฏู…ู‡ ู‡ู„ ู‡ูˆ ุงู„ main ูˆ ู„ุง ุงู„ median ูˆ ู„ุง ุงู„ mode
490
00:41:59,320 --> 00:42:03,800
ุงู† ุดุงุก ุงู„ู„ู‡ for next time ุงุฐุง ุงู„ู…ุฑุฉ ุงู„ุฌุงูŠุฉ ู‡ุชูƒู„ู…
491
00:42:03,800 --> 00:42:10,660
ุนู„ู‰ ู…ูŠู† ุงูุถู„ ู…ู‚ูŠุงุณ ููŠ ู‡ุฏูˆู„ ูˆ ุจุนุฏูŠู† ุจู†ูƒู…ู„ ุฎู„ุงุต
492
00:42:10,660 --> 00:42:15,920
ุนู†ุฏู†ุง two slides ุจุณ ู…ูˆุฌูˆุฏุงุช ูˆ ุจุนุฏูŠู† ู†ุจุฏุฃ ููŠ ุงู„
493
00:42:15,920 --> 00:42:16,900
measures of variation
494
00:42:20,030 --> 00:42:22,550
Any questionุŸ ุงู„ู„ู‡ ุฃูƒุจุฑ