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.

Academic Mathematics NCERT Class 10

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.

Updated on: 10-Oct-2022

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