Test Index

Statistics Part 2

Section: Mathematics

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Question : 17 of 50

Marks: +1, -0

The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are

\mu

\sigma

respectively, then

10(\mu+\sigma)

[7 Apr 2025 Shift 1]

447
445
449
451

Solution:

Let the observations be

x_1, x_2, \dots, x_{99}, 50

\;\;\text{ Mean }\;=\;\frac{x_1+x_2+\dots+x_9+50}{100}=40

\; \Rightarrow \;\; x_1+x_2+\dots+x_{99}=4000-50

\; \Rightarrow \;\; x_1+x_2+\dots+x_{99}=3950

\;\;\text{ Current Mean }\;=\;\frac{3950+40}{100}

\;\mu=\;\frac{399}{10}=39.9

\;(\;\text{ S.D }\;)^2=\sum\limits_{i=1}^{99} \;\frac{(x_i)^2+2500}{100}-(40)^2

\;\sum\limits_{i=1}^{99} x_i^2=160101

\;(\;\text{ Correct S.D }\;)^2=\;\frac{160101+1600}{100}-\left(\;\frac{399}{10}\right)^2

\;\sigma=5

\;10(\mu+\sigma)=10(39.9+5)=449

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