Find the mean, variance and standard deviation using short-cut method

Height in cms No. of children
70-75 3
75-80 4
80-85 7
85-90 7
90-95 15
95-100 9
100-105 6
105-110 6
110-115 3

Asked by Pragya Singh | 11 months ago |  74

1 Answer

Solution :-

\(\)

Mean,

\(\overline{x}= A +\dfrac{\displaystyle\sum_{i=1}{f_i}u_i }{N}× h\)

Where, A = 92.5, h = 5

So, x̅ = 92.5 + ((\( \dfrac{6}{60}\)) × 5)

= 92.5 + \( \dfrac{1}{2}\)

= 92.5 + 0.5

= 93

Then, Variance,

\( σ^2= \dfrac{h^2}{N^2}[N\displaystyle\sum_{i=1}{f_i}u_i^2-(\displaystyle\sum_{i=1}{f_i}u_i)^2] \)

σ2 = \( ( \dfrac{5^2}{60^2})\) [60(254) – 62]

= (\( \dfrac{1}{144}\)) [15240 – 36]

\( \dfrac{15204}{144}\)

\( \dfrac{1267}{22}\)

= 105.583

Hence, standard deviation = σ = \( \sqrt{105.583}\)

= 10.275

Mean = 93, variance = 105.583 and Standard Deviation = 10.275

Answered by Abhisek | 11 months ago

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