Questions: In the data set below, what is the variance? 6, 5, 4, 7, 4, 4 If the answer is a decimal, round it to the nearest tenth. variance (σ^2)

Solution Steps

The mean \( \mu \) of the dataset is calculated as follows:

\[ \mu = \frac{\sum x_i}{n} = \frac{30}{6} = 5.0 \]

The variance \( \sigma^2 \) is computed using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n} \]

Substituting the values, we find:

\[ \sigma^2 = 1.3 \]

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{1.3} \approx 1.2 \]

Final Answer