Question

Find the ‘mean’ and ‘mode’ of the following data:

Class	0 – 15	15 – 30	30 – 45	45 – 60	60 – 75	75 – 90
Frequency	11	8	15	7	10	9

Answer 1

Class	Frequency (f)	Mid-value (x)	fx
0 – 15	11	7.5	82.5
15 – 30	8 → f0	22.5	180
30 – 45	15 → f1	37.5	562.5
45 – 60	7 → f2	52.5	367.5
60 – 75	10	67.5	675
75 – 90	9	82.5	742.5
	`sumf = 60`		`sumfx = 2610`

Mean = `(sumfx)/(sumf)`

= `2610/60`

= 43.5

So, the mean of the given data is 43.5.

Mode:

The class 30 – 45 has the highest frequency of 15.

f₁ = 15, f₀ = 8, f₂ = 7

l = 30, h = 45 – 30 = 15

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

= `30 + ((15 - 8))/((2 xx 15 - 8 - 7)) xx 15`

= `30 + (7 xx 15)/15`

= 30 + 7

= 37

Therefore, the mode of the given data is 37.