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 (Average speed of vehicles (km/hr))	Continuous classes	Frequency (Number of workers)	Cumulative frequency  less than the upper limit
60 - 64	59.5 - 64.5	10	10
64 - 69	64.5 - 69.5	34	44
70 - 74	69.5 - 74.5	55	99 → cf
75 - 79	74.5 - 79.5	85 → f	184
79 - 84	79.5 - 84.5	10	194
84 - 89	84.5 - 89.5	6	200
Total		N = 200

Here, total frequency = ∑f_i = N = 200 

∴ `"N"/2 = 200/2 = 100`

Cumulative frequency, which is just greater than (or equal) to 100, is 184. 

∴ The median class is 74.5 – 79.5.

Now, L = 74.5, f = 85, cf = 99, h = 5

Now,

∴ Median = `"L" + (("N"/2 - "cf")/"f") × "h"`

= `74.5 + ((100 - 99)/85) xx 5`

= `74.5 + 1/85 xx 5`

= `74.5 + 1/17` 

= 74.5 + 0.0588

= 74.558 ≈ 75

∴ The median of the given data is 75 km/hr.