Question

find the variance of the data. 97, 122, 143, 155, 138 (overline{x}=131) variance ((sigma^{2})=)

Explanation:

Step1: Calculate each data - mean difference squared

For \(97\): \((97 - 131)^2=(- 34)^2 = 1156\)
For \(122\): \((122 - 131)^2=(-9)^2 = 81\)
For \(143\): \((143 - 131)^2=(12)^2 = 144\)
For \(155\): \((155 - 131)^2=(24)^2 = 576\)
For \(138\): \((138 - 131)^2=(7)^2 = 49\)

Step2: Calculate the variance

The formula for variance \(\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n}\), where \(n = 5\) and \(\sum_{i = 1}^{5}(x_{i}-\bar{x})^{2}=1156 + 81+144 + 576+49\)
\(\sum_{i = 1}^{5}(x_{i}-\bar{x})^{2}=1156+81 + 144+576+49=2006\)
\(\sigma^{2}=\frac{2006}{5}=401.2\)

Answer:

\(401.2\)