Question

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

Class	15 – 20	20 – 25	25 – 30	30 – 35	35 – 40	40 – 45
Frequency	6	16	17	4	5	2

Answer 1

Class	Frequency (fi)	Class mark (xi)	fixi
15 – 20	6	17.5	105
20 – 25	16 → f0	22.5	360
25 – 30	17 → f1	27.5	467.5
30 – 35	4 → f2	32.5	130
35 – 40	5	37.5	187.5
40 – 45	2	42.5	85
Total	`sumf_i = 50`		`sumf_ix_i = 1335`

We know that

Mean = `(sumf_ix_i)/(sumf_i)`

= `1335/50`

= 26.7

So, the mean of given data is 26.7.

Mode:

The maximum class frequency = 17

The class corresponding to this frequency = 25 – 30

The modal class = 25 – 30

Lower limit (l) = 25

Class size (h) = 30 – 25 = 5

Frequency (f₁) of the modal class = 17

Frequency (f₀) of class preceding the modal class = 16

Frequency (f₂) of class succeeding the modal class = 4

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

= `25 + ((17 - 16)/(2 xx 17 - 16 - 4)) xx 5`

= `25 + (1/(34 - 20)) xx 5`

= `25 + (1/14) xx 5`

= `25 + 5/14`

= 25 + 0.375

= 25.3571

= 25.36

Therefore, the mode of the given data is 25.36.