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The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38 \sigma^{2}$ is equal to____________.
Option: 1
$238$

Option: 2
-

Option: 3
-

Option: 4
-

Answers (1)

best_answer

$\mathrm{\text { Mean }=30} \\$

$\mathrm{\Rightarrow \frac{\sum x}{40}=30 \Rightarrow \sum x=1200} \\$

$\mathrm{\text { Variance }=25} \\$

$\mathrm{\Rightarrow \frac{\sum x^{2}}{40}-30^{2}=25} \\$

$\mathrm{\Rightarrow \sum x^{2}=37000 }\\$

$\mathrm{\text { Correct } \sum x=1200-12-10=1178} \\$

$\mathrm{\text { Correct } \sum x^{2}=37000-144-100=36756 }$

$\therefore 38 \sigma^{2} =38\left[\frac{36756}{38}-\left(\frac{1178}{38}\right)^{2}\right] \\$

$=238$

Hence answer is 238

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rishi.raj

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