Question

Find the arithmetic mean using step deviation method for the following. The data shows distance covered by $40$ passengers to perform their work. (Round off your answer to the nearest whole number).

Distance (km)	1-5	5-9	9-13	13-17	17-21	21-25	25-29
Number of passengers	2	4	6	8	10	5	5

• A. $15$
• B. $16$
• C. $17$
• D. $19$

Answer 1

The correct option is C $17$

Distance (km)	Mid point $x$	Number of passengers $f$	$i$=class interval width	$A$= Assumed mean	$u=\frac{x-A}{i}$	$fu$
1-5	3	2	4	11	-2	-4
5-9	7	4	4	11	-1	-4
9-13	11	6	4	11	0	0
13-17	15	8	4	11	1	8
17-21	19	10	4	11	2	20
21-25	23	5	4	11	3	15
25-29	27	5	4	11	4	20
		$\Sigma f=40$				$\Sigma fu=55$

The formula used for arithmetic mean of grouped data by step deviation method is, $\overline{x}=A+\frac{\sum fu}{\sum f}\times i$
A = Assumed mean of the given data
$\sum$ = Summation of the frequencies given in the grouped data
$\sum fu$ = Summation of the frequencies and deviation of a given mean data
$u=\frac{(x-A)}{i}$
$i=$ Class interval width
$\overline{x}$ = arithmetic mean
$\overline{x}=11+\frac{55}{40}\times 4$
$=11+5.5$
$=16.5$ $\approx$ $17$