Question

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

Duration of calls (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 the mean duration of telephone calls received at the telephone exchange.

Answer 1

Duration of calls (in sec)	Class Marks $\left(x_i\right)$	No. of calls $\left(f_i\right)$	$\left(f_i\right)$$\left(x_i\right)$
15-29	22	8	176
30-44	37	12	444
45-59	52	61	3172
60-74	67	153	10251
75-89	82	190	15580
90-104	97	57	5529
105-119	112	10	1120
120-134	127	9	1143
Total	-	$\sum _{}^{}{f}_i=500$	$\sum _{}^{}{f}_i{x}_i=37415$

$\mathrm{Mean}=\overline{x}=\frac{{\displaystyle \sum _{}^{}}{f}_i{x}_i}{{\displaystyle \sum _{}^{}}{f}_i}=\frac{37415}{500}=74.83$

Therefore, mean duration of telephone calls received at the telephone exchange is 74.83 seconds.