Question

The distances covered by 250 public transport buses in a day is shown in the following frequency distribution table. Find the median of the distance.

Distance (km)	200 - 210	210 - 220	220 - 230	230 - 240	240 - 250
No. of buses	40	60	80	50	20

Answer 1

Class (Distance in Kms)	Frequency (Number of buses) fi	Cumulaive frequency less than the upper limit
200 - 210	40	40
210 - 220	60	100
220 - 230 (Median Class)	80	180
230 - 240	50	230
240 - 250	20	250
	N = 250

From the above table, we get
L (Lower class limit of the median class) = 220
N (Sum of frequencies) = 250
h (Class interval of the median class) = 10
f (Frequency of the median class) = 80
cf (Cumulative frequency of the class preceding the median class) = 100
Now, Median = $L+\left(\frac{{\displaystyle \frac{N}{2}-cf}}{f}\right)\times h$
​$=220+\left(\frac{{\displaystyle \frac{250}{2}-100}}{80}\right)\times 10$
= 220 + 3.13
= 223.13 km
Hence, the median of the distances is 223.13 km.