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Find the Mean, Median and Mode of the Following Data: Classes: 0-20 20-40 40-60 60-80 80-100 100-120 120-140 - Mathematics

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

Classes: 0-20 20-40 40-60 40-60 80-100 100-120 120-140
Frequency: 6 8 10 12 6 5 3

 

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Solution

Consider the following data.

Class Frequency (fi) xi fi xi C.f.
0−20 6 10 60 6
20−40 8 30 240 14
40−60 10 50 500 24
60−80 12 70 840 36
80−100 6 90 540 42
100−120 5 110 550 47
120−140 3 130 390 50
  `N=sumf=50`   `sumf_1x_1=3120`  

Here, the maximum frequency is 12 so the modal class is 60−80.

Therefore,

l = 60

h = 20

f = 12

f1 = 10

f2 = 6

F = 24

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

`=60+(25-24)/12xx20`

`=60+1/12xx20`

`=60+20/12`

= 60 + 1.67

= 61.67

Thus, the median of the data is 61.66.

 

Mean `=(sumf_1x_1)/sumf`

`=3120/50=32.4`

Thus, the mean of the data is 62.4.

 

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

`=60+(12-10)/(24-10-6)xx20`

`=60+2/8xx20`

`=60+40/8`

= 60 + 5

= 65

Thus, the mode of the data is 65.

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 15 Statistics
Exercise 15.5 | Q 15 | Page 47
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