Question

Frequency distribution of duration of $500$ telephone calls received at a telephone exchange on a certain day is given below :

Duration of call (in sec.)	15 - 29	30 - 44	45 - 59	60 - 74	75 - 89	90 - 104	105 - 119	120 - 134
No. of calls	8	12	61	153	190	57	10	9

Find mean duration of telephone call received at the telephone exchange.

• A. $74.83$ seconds
• B. $79.83$ seconds
• C. $83.83$ seconds
• D. $86.83$ seconds

Answer 1

Answer: (A)

$74.83$ seconds

$ci$	$f_i$	$x_i$	$f_i{x}_i$
14.5-29.5	8	22	176
29.5-44.5	12	37	444
44.5-59.5	61	52	3172
59.5-74.5	153	67	10251
74.5-89.5	190	82	15580
89.5-104.5	57	97	5529
104.5-119.5	10	112	1120
119.5-134.5	9	127	1143

$N=\Sigma f_i=500$

$\Sigma f_i{x}_i=37415$

Mean $\overline{x}=\frac{\Sigma f_i{x}_i}{N}$

$\therefore \overline{x}=\frac{37415}{500}=74.83$

Hence, option $A$ is correct.