The following is the frequency distribution of duration for 100 calls made on a mobile phone.

Calculate the average duration (in sec) of a call and also find the median from a cumulative frequency curve.

First, we calculate class marks as follows

Here, (assumed mean) a = 170

and (class width) h = 30

By step deviation method,

Average

= 170 + 0.3 = 170.3

Hence, average duration is 170.3s.

For calculating median from a cumulative frequency curve

We prepare less than type or more than type ogive

We observe that, number of calls in less than 95 s is 0. Similarly, in less than 125 s include the number of calls in less than 95 s as well as the number of calls from 95 - 125 s So, the total number of calls than 125 s is 0 + 14 = 14. Continuing in this manner, we will get remaining in less than 155, 185, 215 and 245 s.

Now, we construct a table for less than ogive (cumulative frequency curve).

To draw less than ogive we plot them the points (95, 0), (125, 14) (155, 36), (185, 64), (215, 85), (245, 100) on the paper and join them by free hand.

∴ Total number of calls (n) = 100

∴ n/2 = 100/2 = 50

Now, point 50 taking on Y - axis draw a line parallel to X - axis meet at a point P and draw a perpendicular line from P to the X - axis, the intersection point of X - axis is the median.

Hence, required median is 170.

13