Question

The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data.

Average Speed of Vehicles(Km/hr)	60 - 64	64 - 69	70 - 74	75 - 79	79 - 84	84 - 89
No. of vehicles	10	34	55	85	10	6

Answer 1

Class (Number of working hours)	Frequency (Number of workers)	Cumulaive frequency less than the upper limit
60 - 64	10	10
64 - 69	34	44
70 - 74 (Median Class)	55	99
75 - 79	85	184
79 - 84	10	194
84 - 89	6	200
	N = 200

From the above table, we get
L (Lower class limit of the median class) = 70
N (Sum of frequencies) = 200
h (Class interval of the median class) = 4
f (Frequency of the median class) = 55
cf (Cumulative frequency of the class preceding the median class) = 44
Now, Median = $L+\left(\frac{{\displaystyle \frac{N}{2}-cf}}{f}\right)\times h$
​$=70+\left(\frac{{\displaystyle \frac{200}{2}-44}}{55}\right)\times 4$
= 70 + 4.09
= 74.09
= 75 vehicles
Hence, the median of data is 75 vehicles.