Question

The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of data.

No. of Mangoes	50 - 100	100 - 150	150 - 200	200 - 250	250 - 300
No. of trees	33	30	90	80	17

 

Answer 1

Class (Number of working hours)	Frequency (Number of workers)	Cumulative frequency  less than the upper limit
50 - 100	33	33
100 - 150	30	63
150 - 200 (Median Class)	90	153
200 - 250	80	233
250 - 300	17	250
	N = 250

From the above table, we get

L (Lower class limit of the median class) = 150

N (Sum of frequencies) = 250

h (Class interval of the median class) = 50

f (Frequency of the median class) = 90

cf (Cumulative frequency of the class preceding the median class) = 63

Now, Median = `L + ((N/2 - cf)/f) xx h`

= `150 + ((250/2 - 63)/90) xx 50`

= `150 + ((125 - 63)/90) xx 50`

= `150 + (62/9) xx 5`

= `150 + 310/9`

= 150 + 34.44

= 184.44 mangoes

= 184 mangoes

Hence, the median of data is 184 mangoes.