QJEEM22Ma1985: JEE Main 2022 Mathematics - Class 11 JEEM22Ma1985 Solution: The mean and standard deviation of 15 observations are found to …

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QJEEM22Ma1985: JEE Main 2022 Mathematics - Class 11 JEEM22Ma1985 Solution: The mean and standard deviation of 15 observations are found to …

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _____________.

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Accepted Answer

$\frac{\sum x_{i}^{2}}{15} - 8^{2} = 9 \Rightarrow \sum x_{i}^{2} = 15 \times 73 = 1095$

Let ${\overset{―}{x}}_{c}$ be corrected mean ${\overset{―}{x}}_{c}$ = 9

$\sum x_{c}^{2} = 1095 - 25 + 400 = 1470$

Correct variance $= \frac{1470}{15} - (9)^{2} = 98 - 81 = 17$

QJEEM22Ma1985: JEE Main 2022 Mathematics - Class 11 JEEM22Ma1985 Solution: The mean and standard deviation of 15 observations are found to …

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