Question

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

Daily income (in Rs)	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

Class interval	Mid value(x)	Frequency(f)	fx	Cumulative frequency
100 - 120	110	12	1320	12
120 - 140	130	14	1820	26
140 - 160	150	8	1200	34
160 - 180	170	6	1020	40
180 - 200	190	10	1900	50
		N = 50	`sumfx=7260`

Mean `=(sumfx)/N=7260/50=145.2`

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 (f) = 14

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

Frequency of class succeeding the modal class (f₂) = 8

Mode `=l+(f-f1)/(2f-f1-f2)xxh`

`=120+(14-12)/(2xx14-12-8)xx20`

`=120+2/(28-20)xx20`

`=120+2/8xx20`

`=120+40/8`

= 120 + 5

= 125

Thus, the mode of the given data is 125.

Here, number of observations N = 50

So, N/2 = 50/2 = 25

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.) or (F) = 12

Frequency of median class(f) = 14

Median `=l+(N/2-F)/fxxh`

`=120+(25-12)/14xx20`

`=120+13/14xx20`

`=120+13/7xx10`

`=120+130/7`

= 120 + 18.57

= 138.57

Thus, the median of the given data is 138.57.