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Question

Find the mean, median and mode of the following data:
Classes:05050100100150150200200250250300300350
Frequency:2356531

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Solution

Class intervalMid value
xi
Frequency
fi
fixi cf
05035 2 50 2
5010075 3 225 5
100150125 5 625 10
150200175 6 1050 16
200250225 5 1127 21
250300275 3 825 24
300350325 1 325 25
fi=25 fixi=4225
Mean=fixifi=422525=169

We have N=25.Then,\dfrac{N}{2}=12.5$
So, median class is 150200.


l= lower limit of the modal class

h= size of the class intervals

f= frequency of the modal class

f1= frequency of the class preceding the modal class

f2= frequency of the class succeed in the modal class.


l=150,h=200150=50,f=6,cf=10

Median=l+N2cff×h

Median=150+12.5106×50

Median=150+1256

Median=150+20.83=170.83.

Here maximum frequency is 6, then the corresponding class 150200 is the modal class.

l=150,h=50,f=6,f1=5f2=5

Mode=l+ff12ff1f2×h

Mode=150+652×655×50

Mode=150+502

Mode=150+25=175

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