In the data table below, notice that the \(x_k\) column would be the given data values but the column for \(x_k^2\) you could easily compute. Table 1.5.7. Sample Grouped Data
So, \(\Sigma x_k = 9\) and \(\Sigma x_k^2 = 35\text{.}\) Therefore \(\overline{x} = \frac{9}{6} = \frac{3}{2}\) and \(v = \frac{\Sigma x_k^2}{6} - (\overline{x})^2 = \frac{35}{6} - (\frac{3}{2})^2 = \frac{70-18}{12} = \frac{26}{6}\text{.}\)
| \(x_k\) | \(x_k^2\) |
| 1 | 1 |
| -1 | 1 |
| 0 | 0 |
| 2 | 4 |
| 2 | 4 |
| 5 | 25 |
Therefore, \(s^2 = \frac{6}{5} \times v = \frac{26}{5}\text{.}\)