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Find the Mean, Median and Mode of the Following Data: Classes: 0-50 50-100 100-150 150-200 200-250 250-300 300-350 Frequency: 2 3 5 6 5 3 1 - CBSE Class 10 - Mathematics

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Question

Find the mean, median and mode of the following data:

Classes: 0 - 50 50 - 100 100 - 150 150 - 200 200 - 250 250 - 300 300 - 350
Frequency: 2 3 5 6 5 3 1

 

Solution

Class
interval
Mid value()x Frequency(f) fx Cumulative frequency
0 - 50 25 2 50 2
50 - 100 75 3 225 5
100 - 150 125 5 625 10
150 - 200 175 6 1050 16
200 - 250 225 5 1125 21
250 - 300 275 3 825 24
300 - 350 325 1 325 25
    N = 25 `sumfx=4225`  

Here, the maximum frequency is 6 so the modal class 150−200.

Therefore,

l = 150

h = 50

f = 6

f1 = 5

f2 = 5

F = 10

 

Mean `=(sumfx)/N=4225/25=169`

Thus, the mean of the data is 169.

 

We have N = 25 then N/2 = 12.5

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

`=150+(12.5-10)/6xx50`

`=150+2.5/6xx50`

`=150+125/6`

= 150 + 20.83

= 170.83

Thus, the median of the data is 170.83.

 

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

`=150+(6-5)/(2xx6-5-5)xx50`

`=150+1/(12-10)xx50`

`=150+1/2xx50`

`=150+50/2`

= 150 + 25

= 175

Thus, the mode of the data is 175.

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Solution Find the Mean, Median and Mode of the Following Data: Classes: 0-50 50-100 100-150 150-200 200-250 250-300 300-350 Frequency: 2 3 5 6 5 3 1 Concept: Mode of Grouped Data.
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