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Question

The following data shows monthly savings of 100 families. Find the difference of modal and mean monthly savings in rupees.

MonthlyNumbersavings () of families10002000142000300015300040002140005000275000600025


A
₹ 916.67
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B
₹ 600.77
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C
₹ 945.55
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D
₹ 840
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Solution

The correct option is D ₹ 840

Modal Class (class with highest frequency) is 4000 - 5000.

Mode=l+(f1f02f1f0f2)×h
where f1 represents the frequency of the modal class.
Also,
l=lower boundary of the modal class
h= size of the modal class interval
f0= frequency of the class preceding the modal class
f2= frequency of the class succeeding the modal class

Here, f1=27,f0=21,f2=25,I=4000,h=1000

Mode=4000+68×1000

=4750

For finding mean, we use Direct method
(We used Direct method to find the mean because the numbers are very easy even though they are large. You could use any of the three methods.)

Mean=ΣfxΣf

=3910

Difference between mode and mean is:
=4750 3910=840


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