Question 821
CBSE Class 11 Mathematics · Statistics · Variance and standard deviation
Values 92,93,97,98,102,104,109 have frequencies 3,2,3,2,6,3,3. Find variance and standard deviation.
Solution to Question 821
Complete workingForm the required totals explicitly and divide by the full number of observations.
\[\begin{aligned}N &= 22,\quad\sum f_ix_i\\&= 2200,\quad\bar x\\&= 100\end{aligned}\]
\[\sum f_i(x_i-100)^2=640\]
\[\sigma^2=\frac{640}{22}\approx29.09,\quad\sigma\approx5.39\]
The variance is nonnegative and the reported standard deviation is its positive square root.
Final answer
\[\sigma^2\approx29.09,\quad\sigma\approx5.39\]