JEE Main 2022 · 26 Jul · Shift 2 · Mathematics Q26

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MathematicsInteger+4 / -1Question 26 of 90

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 ______.

Your answer

Answer and worked solution

Official answer: 238

Totals. $\sum x=1200$ , $\sum x^2=40(25+900)=37000$ .

Remove 12 and 10. $\sum x=1178$ (mean 31), $\sum x^2=36756$ , $n=38$ .

Variance. $38\sigma^2=36756-38\cdot31^2=238$ .

Answer: 238

Topics:Variance and standard deviation

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JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 26