Question

Find the mean, median and mode of the following data: 

Class	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
Frequency	4	4	7	10	12	8	5

Answer 1

To find the mean let us put the data in the table given below:

Class	Frequency `bb((f_i))`	Class mark `bb((x_i))`	`bb(f_i x_i)`
0 – 10	4	5	20
10 – 20	4	15	60
20 – 30	7	25	175
30 – 40	10	35	350
40 – 50	12	45	540
50 – 60	8	55	440
60 – 70	5	65	325
Total	`bb(Ʃ f_i = 50)`		`bb(Ʃ f_i x_i)` = 1910

Mean = `(sum _ i  f_i x_i)/(sum _ i f_i)`

= `1910/50`

= 38.2

Thus, the mean of the given data is 38.2.

Now, to find the median let us put the data in the table given below:

Class	Frequency `(f_i)`	Cumulative Frequency (cf)
0 – 10	4	4
10 – 20	4	8
20 – 30	7	15
30 – 40	10	25
40 – 50	12	37
50 – 60	8	45
60 – 70	5	50
Total	N = `bb(Σ f_i)` = 50

Now, N = 50 ⇒ `"N"/2 =25.`

The cumulative frequency just greater than 25 is 37 and the corresponding class is 40 – 50.

Thus, the median class is 40 – 50.

∴ l = 40, h = 10, N = 50, f = 10 and cf = 25.

Now,

Median = l + `(("N"/2-"cf")/("f")) xx "h"`

= 40 + `((25-15)/10 )xx 10`

= 40

Thus, the median is 40.

We know that,

Mode = 3(median) – 2(mean)

= 3 × 40 – 2 × 38.2

= 120 – 76.4

= 43.6

Hence, Mean = 38.2, Median = 40 and Mode = 43.6