Question

Calculate the mean, median and standard deviation of the following distribution

Class interval:	31-35	36-40	14-45	46-50	51-55	56-60	61-65	66-70
Frequency:	2	3	8	12	16	5	2	3

Answer 1

Given, The data is given in table

To Find: Find the standard deviation

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

Explanation:

Now, N=50, \(\Sigma u_if_i\) = - 30, \(\Sigma u^2_if_i\) = 134

Mean \(\bar X\) = A +h \(\Big(\frac{\Sigma u_if_i}{N}\Big)\) 

  \(\bar X\) = 53 + 5\(\Big(-\frac{30}{50}\Big)\) 

  \(\bar X\) = 50

Variance = 58

Standard Deviation σ = \(\sqrt{58}\)  

SD = 7.62 

Hence, The standard deviation is 7.62