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
| \(x_k\) |
\(x_k^2\) |
| 1 |
1 |
| -1 |
1 |
| 0 |
0 |
| 2 |
4 |
| 2 |
4 |
| 5 |
25 |
So,
\(\Sigma x_k = 9\) and
\(\Sigma x_k^2 = 35\text{.}\) Therefore
\(\overline{x} = \frac{9}{6} = \frac{3}{2}\) and
\(v = \frac{\Sigma x_k^2}{6} - (\overline{x})^2 = \frac{35}{6} - (\frac{3}{2})^2 = \frac{70-18}{12} = \frac{26}{6}\text{.}\)