Questions: Question 3 What is the standard deviation? This is sample data 12,13,15,16,24,15,22,10,9,13,13,18,16,25,23,24 Round to two decimals

Solution Steps

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

\[ \mu = \frac{\sum x_i}{n} = \frac{268}{16} = 16.75 \]

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

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} = 27.93 \]

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

\[ \sigma = \sqrt{27.93} = 5.29 \]

Final Answer