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.

Given:

The given table gives the daily income of 50 workers of a factory.

To do:

We have to find the mean, mode and median of the above data.

Solution:

The frequency of the given data is as given below.

Let the assumed mean be $A=150$.

We know that,

Mean $=A+h \times \frac{\sum{f_id_i}}{\sum{f_i}}$

Therefore,

Mean $=150+20\times(\frac{-12}{50})$

$=150-20(0.24)$

$=150-4.8$

$=145.2$

The mean of the given data is Rs. 145.20.

We observe that the class interval of 120-140 has the maximum frequency(14).

Therefore, it is the modal class.

Here,

$l=120, h=20, f=14, f_1=12, f_2=8$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=120+\frac{14-12}{2 \times 14-12-8} \times 20$

$=120+\frac{2}{28-20} \times 20$

$=120+\frac{40}{8}$

$=120+5$

$=125$

The mode of the given data is Rs. 125.

Here,

$N=50$

This implies, $\frac{N}{2}=\frac{50}{2}=25$

Median class $=120-140$

We know that,

Median $=l+\frac{\frac{N}{2}-F}{f} \times h$

$=120+\frac{25-12}{14} \times 20$

$=120+\frac{13 \times 20}{14}$

$=120+\frac{130}{7}$

$=120+18.57$

$=138.57$

The median of the given data is Rs. 138.57.

The mean, mode and median of the above data are Rs. 145.20, Rs. 125 and Rs. 138.57 respectively.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

31 Views

Kickstart Your Career

Get certified by completing the course

Get Started