Question

find the variance of the data.
16, 31, 38, 24, 36
\\( \overline { x } = 29 \\)
variance \\( ( \sigma ^ { 2 } ) = ? \\)

Explanation:

Step1: Calculate each data point's deviation from the mean

For \(16\): \(16 - 29=- 13\)
For \(31\): \(31 - 29 = 2\)
For \(38\): \(38 - 29=9\)
For \(24\): \(24 - 29=-5\)
For \(36\): \(36 - 29 = 7\)

Step2: Square each deviation

\((-13)^2=169\)
\(2^2 = 4\)
\(9^2=81\)
\((-5)^2 = 25\)
\(7^2=49\)

Step3: Find the average of the squared deviations

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Answer:

\(65.6\)