Question

If the arithmetic mean of the data given below is 28, find the median of the series:

Profit per retail shop (in Rs)	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Number of retail shops	12	18	27	-	17	6

Answer 1

Class Interval	Frequency (f)	Cumulative Frequency (CF)
0 - 10	12	12
10 - 20	18	30
20 - 30	27	57
30 - 40	20	77
40 - 50	17	94
50 - 60	6	100
Total	`sumf=100`

`sumf="N"=100`

So, the Median class = Size of `("N"/2)^"th"` item

= 50^th item

50^th item lies in the 57^th cumulative frequency and the corresponding class interval is 20 - 30.

Median `=L+(N/2-CF)/fxxi`

`=20+(100/2-30)/27xx10`

`=20+(50-30)/27xx10`

`=20+20/27xx10`

= 27.40