In an experiment with 15 observations on x, the following results were available. \sum x^{2}=2830,\; \sum x=170  One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is

  • Option 1)

    188.66

  • Option 2)

    177.33

  • Option 3)

    8.33

  • Option 4)

    78.00

 

Answers (1)

As we learnt in 

Variance -

In case of discrete data 

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

-

 

 \sum x_i^2=\:2830, \:\sum x_i=170

\sum x_i(new)= 170-20+30\:=180

\sum x_i^2(new)= 2830-20^2+30^2=3330

Variance_{(new)}\:=\frac{3330}{15} -\left(\frac{180}{15} \right )^{2}

=222-144 = 78


Option 1)

188.66

Incorrect

Option 2)

177.33

Incorrect

Option 3)

8.33

Incorrect

Option 4)

78.00

Correct

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