Question

The following table shows the absentee records of 40 students in an academic year:

Number of Days	Number of Students
2 − 6	11
6 − 10	10
10 − 14	7
14 − 18	4
18 − 22	4
22 − 26	3
26 − 30	1

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

Answer 1

Number of Days	Number of Students (f)	Mid value (x)	fx
2 − 6	11	4	44
6 − 10	10	8	80
10 − 14	7	12	84
14 − 18	4	16	64
18 − 22	4	20	80
22 − 26	3	24	72
26 − 30	1	28	28
Total	`sumf = 40`		`sumfx = 452`

Mean = `(sumfx)/(sumf)`

= `452/40`

= 11.3

So, the mean of the given data is 11.3.

Mode:

The highest frequency is 11. Therefore, the modal class is 2 – 6.

∴ f₁ = 11, f₂ = 10, f₀ = 0

l = 2, h = 4

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

= `2 + ((11 - 0)/(2 xx 11 - 0 - 10)) xx 4`

= `2 + 11/12 xx 4`

= 2 + 3.67

= 5.67

Therefore, the mode of the given data is 5.67.