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 ___________.
Answer (integer)
238
Solution
<p>$\mu = {{\sum {{x_i}} } \over {40}} = 30 \Rightarrow \sum {{x_i} = 1200}$</p>
<p>$${\sigma ^2} = {{\sum {x_i^2} } \over {40}} - {(30)^2} = 25 \Rightarrow \sum {x_i^2 = 37000} $$</p>
<p>After omitting two wrong observations</p>
<p>$\sum {{y_i} = 1200 - 12 - 10 = 1178}$</p>
<p>$\sum {y_i^2 = 37000 - 144 - 100 = 36756}$</p>
<p>Now $${\sigma ^2} = {{\sum {y_i^2} } \over {38}} - {\left( {{{\sum {{y_i}} } \over {38}}} \right)^2}$$</p>
<p>$= {{36756} \over {38}} - {\left( {{{1178} \over {38}}} \right)^2} = - {31^2}$</p>
<p>$= 38{\sigma ^2} = 36756 - 36518 = 238$</p>
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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