Find the mean and standard deviation using short-cut method

 xi 60 61 62 63 64 65 66 67 68 fi 2 1 12 29 25 12 10 4 5

Asked by Abhisek | 11 months ago |  74

##### Solution :-

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

Where A = 64, h = 1

So, x̅ = 64 + (($$\dfrac{0}{100}$$) × 1)

= 64 + 0

= 64

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 = ($$\dfrac{1^2}{100^2}$$) [100(286) – 02]

= ($$\dfrac{1}{10000}$$) [28600 – 0]

$$\dfrac{28600}{10000}$$

= 2.86

Hence, standard deviation = σ =$$\sqrt{2.886}$$

= 1.691

Mean = 64 and Standard Deviation = 1.691

Answered by Abhisek | 11 months ago

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