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) fi	Cumulaive 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 = $L+\left(\frac{{\displaystyle \frac{N}{2}-cf}}{f}\right)\times h$
​$=150+\left(\frac{{\displaystyle \frac{250}{2}-63}}{90}\right)\times 50$
= 150 + 34.44
= 184.44 mangoes
= 184 mangoes
Hence, the median of data is 184 mangoes.