Question:
Marks of 5 students of a group are \( 8, 12, 13, 15, 22 \). Find the variance.
Marks of 5 students of a group are \( 8, 12, 13, 15, 22 \). Find the variance.
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To find the variance, first calculate the mean, then determine the squared deviations from the mean, and finally divide the sum of these squared deviations by the total number of data points.
Updated On: Jan 22, 2025
- \( 22.1 \)
- \( 23.0 \)
- \( 20.2 \)
- \( 21.2 \)
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The Correct Option is D
Solution and Explanation
Step 1: Compute the mean (\( \bar{x} \)) of the given data.
\[
\bar{x} = \frac{\sum x_i}{n} = \frac{8 + 12 + 13 + 15 + 22}{5} = 14.
\]
Step 2: Calculate the squared deviations from the mean.
\[
(x_i - \bar{x})^2 = \{(8-14)^2, (12-14)^2, (13-14)^2, (15-14)^2, (22-14)^2\}.
\]
\[
(x_i - \bar{x})^2 = \{36, 4, 1, 1, 64\}.
\]
Step 3: Find the variance.
\[
\text{Variance (Var(x))} = \frac{\sum (x_i - \bar{x})^2}{n} = \frac{36 + 4 + 1 + 1 + 64}{5} = \frac{106}{5} = 21.2.
\]
Final Answer:
The variance of the data is:
\[
\boxed{21.2}
\]
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