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Question
Find the mean, variance and standard deviation using short-cut method
Height in cm70−7575−8080−8585−9090−9595−100100−105105−110110−115No. of children3477159663
Find the mean, variance and standard deviation using short-cut method
Height in cm70−7575−8080−8585−9090−9595−100100−105105−110110−115No. of children3477159663
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Solution
HeightMid valuesin cms.xifiu=x−92.55fufu2 70−75 72.5 3−4−1248 75−80 77.5 4−3−1236 80−85 82.5 7−2−1428 85−90 87.5 7−1−7 7 90−95 92.515 0 0 0 95−100 97.5 9 1 9 9100−105102.5 6 2 1224105−110107.5 6 3 1854110−115112.5 3 4 1248606254
Mean (¯¯¯x)=A+∑fuN×h=92.5+660×5=92.5+0.5=93
Variance (σ2)=h2N2[N∑fu2−(∑fu)2]=(5)2(60)2[60×254−(6)2]
=253600[15240−36]=253600×15204=105.58
Standard deviation (σ)=√105.58=10.27
HeightMid valuesin cms.xifiu=x−92.55fufu2 70−75 72.5 3−4−1248 75−80 77.5 4−3−1236 80−85 82.5 7−2−1428 85−90 87.5 7−1−7 7 90−95 92.515 0 0 0 95−100 97.5 9 1 9 9100−105102.5 6 2 1224105−110107.5 6 3 1854110−115112.5 3 4 1248606254
Mean (¯¯¯x)=A+∑fuN×h=92.5+660×5=92.5+0.5=93
Variance (σ2)=h2N2[N∑fu2−(∑fu)2]=(5)2(60)2[60×254−(6)2]
=253600[15240−36]=253600×15204=105.58
Standard deviation (σ)=√105.58=10.27
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