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 | 1 year ago |  89

##### 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 | 1 year ago

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