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 (integer)
17
Solution
<p>$${{\sum {x_i^2} } \over {15}} - {8^2} = 9 \Rightarrow \sum {x_i^2 = 15 \times 73 = 1095} $$</p>
<p>Let ${\overline x _c}$ be corrected mean ${\overline x _c}$ = 9</p>
<p>$\sum {x_c^2 = 1095 - 25 + 400 = 1470}$</p>
<p>Correct variance $= {{1470} \over {15}} - {(9)^2} = 98 - 81 = 17$</p>
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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