TS ICET 2017 Question Paper with Solutions for online practice

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Question : 141 of 200

Marks: +1, -0

What is the Mean of the following distribution ?

x	1	2	3	......	100
f	1	4	9	......	10000

4050
5000
5050
5075
None of the above

Solution:

Here,

x_i=n

f_i=n2

Mean

=\;\;{∑x_{i}f_{i}}/{Σf_{i}}=\;\;{Σn.n^{2}}/{Σn^{2}}=\;\;{Σn^{3}}/{Σn^{2}}

=\;\;{[\;\;{n(n+1)}/{2}]}/{[\;\;{n(n+1)(2n+1)}/{6}]}=\;\;{3}/{2}\;\;{n(n+1)}/{(2n+1)}

Here, n = 100
∴ Required mean

=3/2×{100×10!}/20!=5050/67≈75.4

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