Questions: Find the variance of the data. 97, 122, 143, 155, 138 x̄=131 Variance (σ^2)=[?]

Solution Steps

First, we calculate the deviation of each data point from the mean \(\bar{x} = 131\).

\[ \begin{align_} 97 - 131 &= -34, \\ 122 - 131 &= -9, \\ 143 - 131 &= 12, \\ 155 - 131 &= 24, \\ 138 - 131 &= 7. \end{align_} \]

Next, we square each of the deviations calculated in Step 1.

\[ \begin{align_} (-34)^2 &= 1156, \\ (-9)^2 &= 81, \\ 12^2 &= 144, \\ 24^2 &= 576, \\ 7^2 &= 49. \end{align_} \]

Now, we find the mean of these squared deviations. This is the variance.

\[ \sigma^2 = \frac{1156 + 81 + 144 + 576 + 49}{5} = \frac{2006}{5} = 401.2 \]

Final Answer