Question

Find the mean of following frequency distribution using step deviation method.

• A. $44.66$
• B. $40.66$
• C. $42.66$
• D. $45.66$

Answer 1

The correct option is C $42.66$

Answer:-

Class interval width $\left(W\right)=21-11=10$

Converting the given data into frequency distribution table:

1. Write the mid-point of each interval $\left(X_i\right)$.

2. Consider any value of the $X_i$ as $A$ or Assumed mean.

3. Find deviation $\left(d_i\right)$ of each value of $X$ from assumed mean as defined in the table.

4. Multiply each valye of $d_i$ with the corresponding frequency $f_i$.

Class interval	$X_i$	No. of employees $f_i$	$d_i=\frac{X-A}{W}$	$f_i{d}_i$
11-21	16	2	-2	-4
21-31	26	4	-1	-4
31-41	36=A	6	0	0
41-51	46	8	1	8
51-61	56	10	2	20
		$\Sigma f=30$		$\Sigma fd=20$

5. Calculate mean using the formula below:

Mean = $A+\frac{\Sigma fd}{\Sigma f}=36+\frac{20}{30}\times 10=36+6.66=42.66$

Hence, option C is correct.