JEE MAIN - Mathematics (2022 - 28th June Morning Shift - No. 14)
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 _____________.
Answer
17
Explanation
$${{\sum {x_i^2} } \over {15}} - {8^2} = 9 \Rightarrow \sum {x_i^2 = 15 \times 73 = 1095} $$
Let $${\overline x _c}$$ be corrected mean $${\overline x _c}$$ = 9
$$\sum {x_c^2 = 1095 - 25 + 400 = 1470} $$
Correct variance $$ = {{1470} \over {15}} - {(9)^2} = 98 - 81 = 17$$
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