Questions: For the following set of data, find the population standard deviation, to the nearest hundredth. 124,36,26,133,76,73,115

Solution Steps

To find the mean \( \mu \) of the dataset, we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

For the given data \( 124, 36, 26, 133, 76, 73, 115 \), the sum is \( 583 \) and the number of data points \( N \) is \( 7 \). Thus, we have:

\[ \mu = \frac{583}{7} = 83.29 \]

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

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

Substituting the mean \( \mu = 83.29 \) into the formula, we compute the squared differences and their sum, which results in a variance of:

\[ \sigma^2 = 1544.49 \]

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

\[ \sigma = \sqrt{\sigma^2} = \sqrt{1544.49} = 39.3 \]

Final Answer