Questions: For the following set of data, find the population standard deviation. 101, 142, 202, 140, 150, 109, 135, 161, 172

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 \( 101, 142, 202, 140, 150, 109, 135, 161, 172 \), the sum is \( 1312 \) and the number of data points \( N \) is \( 9 \). Thus, we have:

\[ \mu = \frac{1312}{9} \approx 145.78 \]

Next, we calculate the population variance \( \sigma^2 \) using the formula:

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

Substituting the values, we find that the variance is approximately \( 846.62 \). The population standard deviation \( \sigma \) is then calculated as:

\[ \sigma = \sqrt{846.62} \approx 29.1 \]

Final Answer