#### The following is the frequency distribution of duration for100 calls made on a mobile phone : Duration (in seconds) Number of calls 95-125 125-155 155-185 185-215 215-245 14 22 28 21 15 Calculate the average duration (in sec) of a call and also find the median from cumulative frequency curve.

Solution.

 Duration fi xi $u_{i}\frac{\left ( x_{i}-a \right )}{h}$ fiui 95-125 14 110 -2 -28 125-155 22 140 -1 -22 155=185 28 170 = a 0 0 185-215 21 200 1 21 215-245 21 230 2 30 $\sum f_{i}= 100$ $\sum f_{i}u_{i}= 1$

a = 170, h = 30
Average = $a+\frac{\sum f_{i}u_{i}}{\sum f_{i}}\times h= 170+\frac{1}{100}\times 30= 170+0\cdot 3= 170\cdot 3$

 less than type Duration Number of calls less than 95 less than 125 less than 155 less than 185 less than 215 less than 245 0 0+14 = 14 14+22 =36 36 + 28 = 64 64 + 21 = 85 85 + 15 =100

n = 100

$\frac{n}{2}= \frac{100}{2}= 50$
median is 170