Question

Find the standard deviation for the following distribution :

X :	4.5	14.5	24.5	34.5	44.5	54.5	64.5
f:	1	5	12	22	17	9	4

Answer 1

Given, The data is given in table/ 

To Find: Find the standard deviation 

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

Explanation: Here, Mean = \(\Sigma\frac{f_ix_i}{f_i}\) 

Mean = \(\frac{4.5+14.5+24.5 +34.5+44.5+54.5+64.5}{7}\) 

100[1.857-0.0987] 

100[1.7583]

Var(X) = 175.83

Standard Deviation σ = \(\sqrt{Var(X)}\) 

\(\sqrt{175.83}\) 

SD = 13.26 

Hence, The standard deviation is 13.26