Question

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

Marks	0 – 5	5 – 10	10 – 15	15 – 20	20 – 25	25 – 30
Number of students	2	3	8	15	14	8

Answer 1

Marks (C.I.)	No. of students (f)	Midvalue (x)	fx
0 – 5	2	2.5	5
5 – 10	3	7.5	22.5
10 – 15	8 → f0	12.5	100.00
15 – 20	15 → f1	17.5	262.5
20 – 25	14 → f2	22.5	315
25 – 30	8	27.5	220
Total	`bb(sumf = 50)`		`bb(sumfx = 925)`

Mean = `(sumfx)/(sumf)`

= `925/50`

= 18.5

So, the mean of the given data is 18.5.

Mode:

Class 15 – 20 has height frequency of 15.

∴ f₁ = 15, f₀ = 8, f₂ = 14

l = 15, h = 5

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

= `15 + ((15 - 8)/(2 xx 15 - 8 - 14)) xx 5`

= `15 + (7 xx 5)/8`

= `15 + 35/8`

⇒ `(120 + 35)/8`

= `155/8`

= 19.375

Therefore, the mode of the given data is 19.375.