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  • Solve it, The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining obs

The sum of 100 observations and the sum of their squares are 400 and 2475, respectively.  Later on, three observations, 3, 4 and 5, were found to be incorrect.  If the incorrect observations are omitted, then the variance of the remaining observations is :

  • Option 1)

    8.25

  • Option 2)

    8.50

  • Option 3)

    8.00

  • Option 4)

    9.00

 

Answers (1)

best_answer

As we learnt in 

ARITHMETIC Mean -

For the values x1, x2, ....xn of the variant x the arithmetic mean is given by 

\bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}

in case of discrete data.

-

 

Short cut Method for Variance -

In case of discrete frequency distribution 

\sigma ^{2}= \frac{1}{N}\sum_{i=1}^{n}f_{i}d_{i}^{2}-\left ( \frac{1}{N}\sum_{i=1}^{n} f_{i}d_{i}\right )^{2}

-

 

 

\sum x_{i}=400

\frac{\sum x_{i}}{100}=4

Omitting 3, 4, 5 we get \frac{\sum x_{i}}{97}=\frac{400-12}{97}=4

Sum of squares = 2475-50=2425

\frac{\sum x_{i^{2}}}{100}=25

Variance = \frac{\sum x_{i^{2}}}{100}-\left( \frac{\sum x_{i}}{100}\right )^{2}

=25-4^{2}=9


Option 1)

8.25

This option is incorrect

Option 2)

8.50

This option is incorrect

Option 3)

8.00

This option is incorrect

Option 4)

9.00

This option is correct

Posted by

Aadil

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