Question

The variance $\sigma^2$ of the data
Is _______.

Answer 1

Calculate sums:

$\sum f_i = 22, \quad \sum f_i x_i = 176, \quad \sum f_i x_i^2 = 2048.$

Calculate the mean $\bar{x}$:

$\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{176}{22} = 8.$

Calculate the variance $\sigma^2$:

$\sigma^2 = \frac{1}{N} \sum f_i x_i^2 - \bar{x}^2,$

where $N = \sum f_i$.

Plugging in values:

$\sigma^2 = \frac{1}{22} \times 2048 - (8)^2 = \frac{2048}{22} - 64.$

Compute:

$\frac{2048}{22} = 93.09090909 \quad \text{and} \quad \sigma^2 = 93.09090909 - 64 = 29.09090909.$

Thus, the variance is: 29.09090909