Question

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

Class	20 – 25	25 – 30	30 – 35	35 – 40	40 – 45	45 – 50
Frequency	9	8	11	13	4	5

Answer 1

Class	Frequency (fi)	Class marks (xi)	fixi
20 – 25	9	22.5	202.5
25 – 30	8	27.5	220
30 – 35	11 → f0	32.5	357.5
35 – 40	13 → f1	37.5	487.5
40 – 45	4 → f2	42.5	170
45 – 50	5	47.5	237.5
Total	`bb(sumf_i = 50)`		`bb(sumf_ix_i = 1675)`

We know that

Mean = `(sumf_ix_i)/(sumf_i)`

= `1675/50`

= 33.5

So, the mean of the given data is 33.5.

Mode:

The maximum class frequency = 13

The class corresponding to this frequency = 35 – 40

The modal class = 35 – 40

Lower limit (l) = 35

Class size (h) = 40 – 35 = 5

Frequency (f_i) of the modal class = 13

Frequency (f₀) of class preceding the modal class = 11

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

We know that,

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

= `35 + ((13 - 11))/((2 xx 13 - 11 - 4)) xx 5`

= `35 + (2/(26 - 15)) xx 5`

= `35 + 2/11 xx 5`

= `35 + 10/11`

= 35 + 0.90

= 35.90

Therefore, the mode of the given data is 35.90.