Question

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

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

Answer 1

First, we calculate class marks as follows

Here, (assumed mean)a=170
and (class width)h=30
By step deviation method.
`"Average"(bar(x))=a+(sumf_(i)u_(i))/(sumf_(i))xxh=170+(1)/(100)xx30`
=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, the number of calls in less then 95 s as well as the number of calls from 95-125 .s So, the total number of calls in less than 125 s is 0+14=14. Continuing in this manner, we will get remaining in less than 155,185,215 and 245s.
Now, we construct a table for lesst han type ogive (cumulative frequency curve)

To draw less than ogive we plot them the points (95,0),(125,14),(155,36),(185,64),(214,85),(245,100) on the paper and join them by free hand.

`therefore` Total number of calls (n)=100
`(n)/(2)=(100)/(2)=50`
Now, point 50 taking on Y-axis drw 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 X-axis is the meidan, Hence, required median is 170.