Let the random variable \(X\) take values 0 and 2 with frequencies 23 and 17 respectively.

The total number of observations is 40.

The mean \(\bar{x}\) is calculated as:

\(\bar{x} = \frac{(0 \times 23) + (2 \times 17)}{40} = \frac{34}{40} = 0.85\)

The variance \(s^2\) is calculated using:

\(s^2 = \frac{(0^2 \times 23) + (2^2 \times 17)}{40} - (\bar{x})^2\)

\(s^2 = \frac{(0 \times 23) + (4 \times 17)}{40} - (0.85)^2\)

\(s^2 = \frac{68}{40} - 0.7225\)

\(s^2 = 1.7 - 0.7225 = 0.9775\)

\(Thus, the variance is approximately 0.978.\)