Question

find the variance of the data.
251, 224, 237, 255, 268
\\( \overline { x } = 247 \\)
variance \\( ( \sigma ^ { 2 } ) = \\)

Explanation:

Step1: Calculate each data - value minus the mean

For \(251\): \(251 - 247=4\)
For \(224\): \(224 - 247=- 23\)
For \(237\): \(237 - 247=-10\)
For \(255\): \(255 - 247 = 8\)
For \(268\): \(268 - 247=21\)

Step2: Square each of the differences

\(4^{2}=16\)
\((-23)^{2}=529\)
\((-10)^{2}=100\)
\(8^{2}=64\)
\(21^{2}=441\)

Step3: Find the average of the squared differences (variance formula \(\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n}\))

\(\sum_{i = 1}^{5}(x_{i}-\bar{x})^{2}=16 + 529+100 + 64+441=1150\)
Since \(n = 5\), \(\sigma^{2}=\frac{1150}{5}=230\)

Answer:

\(230\)