3 Marks Question

Question 13 Marks

The arithmetic mean of 1, 3, 5, 6, X and 10 is 6, then find the value of X.

Answer

In this question, mean is given as 6 .
The observations are $1,3,5,6, X$ and 10 . So the total no. of observations is 6 . One observation is missing which we take as X .
Mean $=$ Total of all observations $/$ No. of observations
$\begin{array}{l}
\bar{X}=\frac{\Sigma X}{n} \\
\bar{X}=\frac{1+3+5+6+X+10}{6} \\
\Rightarrow \quad 6=\frac{25+X}{6} \Rightarrow 36=25+X \\
\therefore X=36-25=11
\end{array}$

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Question 23 Marks

Mean marks obtained by 100 students are estimated to be 40. Later on it is found that one value was read as 83 instead of 53. Find out the 'corrected' mean.

Answer

Given, $\bar{X}=40, n=100$
Now, $\bar{X}=\frac{\Sigma X}{n} \Rightarrow 40=\frac{\Sigma X}{100}$
$\Rightarrow \quad \Sigma X(\text { wrong })=40 \times 100=4000,$
Also given, correct value $=53$, incorrect value $=83$.
We have to add the correct value and deduct the incorrect value from 4000 and divide it by no. of observations.
$\therefore$ Correct $\bar{X}$
$\begin{array}{l}
=\frac{\Sigma X(W \text { rong })+(\text { Correct value })-(\text { Incorrect value })}{n} \\
=\frac{4000+53-83}{100}=\frac{3970}{100}=39.70
\end{array}$
Thus, corrected mean $=39.70$

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Question 33 Marks

In how many groups, different commodities have been divided while constructing the Wholesale Price Index in India?

Answer

To measure WPI, commodities are classified into the following categories:
1) Primary goods: It covers both food and nonfood items. These goods are directly obtained from natural resources.
2) Fuels: it includes fuel and related products like coal, petroleum, electricity.
3) Manufactured or Industrial good: it includes machinery, equipment, chemicals, fertilizers, etc.

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