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)

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

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