Question

The following table shows the number of traffic challans issued in the month of April by the traffic police:

Number of Challans	Number of Days
0 − 10	3
10 − 20	5
20 − 30	10
30 − 40	9
40 − 50	2
50 − 60	1
Total	30

Find the ‘mean’ and ‘mode’ of the above data.

Answer 1

Number of Challans	Number of Days (δ)	Mid value x	fx
0 − 10	3	5	15
10 − 20	5 → f0	15	75
20 − 30	10 → f1	25	250
30 − 40	9 → f2	35	315
40 − 50	2	45	90
50 − 60	1	55	55
Total	`sumf = 30`		`sumfx = 800`

Mean = `(Σfx)/(Σf)`

= `800/30`

= 26.67

So, the mean of the given data is 26.67.

Mode:

The highest frequency is 10, and it corresponds to the number of challans in the 20 – 30 range.

f₁ = 10, f₀ = 5, f₂ = 9

l = 20, h = 10

Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`

= `20 + ((10 - 5)/(2 xx 10 - 5 - 9)) xx 10`

= `20 + (5 xx 10)/6`

= `20 + 50/6`

= `20 + 25/3`

= `(60 + 25)/3`

= `85/3`

= 28.33

Therefore, the mode of the given data is 28.33.