Collecting this data into a frequency distribution gives
Table 1.6.2. Grouped Discrete Data
| \(x_k\) |
\(f_k\) |
| 1 |
5 |
| 2 |
7 |
| 3 |
4 |
| 4 |
3 |
| 5 |
6 |
Therefore,
\begin{equation*}
\overline{x} = \frac{1 \times 5 + 2 \times 7 + 3 \times 4 + 4 \times 3 + 5 \times 6}{5+7+4+3+6} \\
= \frac{5 + 14 + 12 + 12 + 30}{25} = \frac{43}{25}
\end{equation*}
and
\begin{align*}
v & = \frac{1^2 \times 5 + 2^2 \times 7 + 3^2 \times 4 + 4^2 \times 3 + 5^2 \times 6}{5+7+4+3+6} - \left ( \frac{43}{25} \right )^2 \\
& = \frac{5 + 28 + 36 + 48 + 150}{25} - \left ( \frac{43}{25} \right )^2 \\
& = \frac{4826}{625}\\
& \approx 7.7216
\end{align*}
and so \(s^2 = \frac{25}{24} \frac{4826}{625} \approx 8.043\text{.}\)