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# Solution for The Following Table Gives the Daily Income of 50 Workers of a Factory Find the Mean, Mode and Median of the Above Data. - CBSE Class 10 - Mathematics

#### 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.

#### Solution

 Classinterval 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.

Is there an error in this question or solution?

#### APPEARS IN

Solution The Following Table Gives the Daily Income of 50 Workers of a Factory Find the Mean, Mode and Median of the Above Data. Concept: Mode of Grouped Data.
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