Question

The following table gives the daily income of 50 workers of a factory :

Daily income (in ₹) 100-120 120-140 140-160 160-180 180-200

Number of workers : 12 14 8 6 10

Find the mean, mode and median of the above data .

Answer 1

Let the assumed mean a be 150.

The table for the given data can be drawn as

Class Interval	Number of Workers(fi)	Classmark(xi)	di = xi − 150	fidi	Cumulative Frequency(c.f.)
100−120	12	110	−40	−480	12
120−140	14	130	−20	−280	26
140−160	8	150	0	0	34
160−180	6	170	20	120	40
180−200	10	190	40	400	50
Total	50			−240

Mean is given by .

Thus, the mean of the given data is 145.2.

It can be seen in the data table that the maximum frequency is 14. The class corresponding to this frequency is 120−140.

∴ Modal class = 120 − 140

Lower limit of modal class (l) = 120

Class size (h) = 140 − 120 = 20

Frequency of modal class (f₁) = 14

Frequency of class preceding the modal class (f₁) = 12

Frequency of class succeeding the modal class (f₁) = 8

Mode is given by

Thus, the mode of the given data is 125.

Here, number of observations (n) = 50

This observation lies in class interval 120−140.

Therefore, the median class is 120−140.

Lower limit of median class (l) = 120

Cumulative frequency of class preceding the median class(c.f.) = 12

Frequency of median class(f) = 14

Median of the data is given by

Thus, the median of the given data is 138.57.