1.

Find the standard deviation for the following data X:234567f:491614116

Answer»

Given, The data is given in table

To Find: Find the standard deviation 

The formula used: SD = \(\sqrt{Var(X)}\) 

Explanation:

xififixifixi2
24816
392781
41664256
51470350
61166396
7642294
N = 60Total = 277Total = 1393

Now, N = 60, Σxifi = 277, Σxi2fi = 1393

Mean \(\bar{X}\) = \(\Big(\frac{\Sigma x_if_i}{N}\Big)\) 

  \(\bar{X}\) = \(\frac{277}{60}\) 

  \(\bar{X}\) = 4.62

Var (X) = \(\frac{1393}{60}\) - (4.62)2

Variance = 1.88 

Standard Deviation σ = \(\sqrt{1.88}\) 

SD = 1.37

Hence, The standard deviation is 1.37


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