Question 1181
CBSE Class 11 Mathematics · Statistics · Grouped data
A group of 100 observations was reported with mean 20 and standard deviation 3. Recorded values 21,21,18 must be omitted. Find the corrected mean and standard deviation.
Solution to Question 1181
Complete workingForm the required totals explicitly and divide by the full number of observations.
\[\begin{aligned}\sum x &= 2000,\quad\sum x^2\\&= 100(3^2+20^2)\\&= 40900\end{aligned}\]
\[\begin{aligned}N' &= 97,\quad\sum x'\\&= 2000-21-21-18\\&= 1940\end{aligned}\]
\[\begin{aligned}\bar x' &= \frac{1940}{97}\\&= 20\end{aligned}\]
\[\begin{aligned}\sum x'^2 &= 40900-21^2-21^2-18^2\\&= 39694\end{aligned}\]
\[\sigma'=\sqrt{\frac{39694}{97}-20^2}\approx3.04\]
The variance is nonnegative and the reported standard deviation is its positive square root.
Final answer
\[\bar x'=20,\quad\sigma'\approx3.04\]