\begin{tabular}{l} Question 6 \\ The following set of data is from a sample. \\ 10, 14, \( 5,13,11,14,3 \) \\ Compute the Variance: \\ \hline Add your answer \\ Integer, decimal, or E notation allowed \end{tabular}

To compute the variance of the sample data set \( 10, 14, 5, 13, 11, 14, 3 \), we first calculate the mean (average): 1. **Find the mean:** \[ \text{Mean} = \frac{(10 + 14 + 5 + 13 + 11 + 14 + 3)}{7} = \frac{70}{7} = 10 \] 2. **Calculate the squared differences from the mean:** - \( (10-10)^2 = 0 \) - \( (14-10)^2 = 16 \) - \( (5-10)^2 = 25 \) - \( (13-10)^2 = 9 \) - \( (11-10)^2 = 1 \) - \( (14-10)^2 = 16 \) - \( (3-10)^2 = 49 \) 3. **Sum the squared differences:** \[ 0 + 16 + 25 + 9 + 1 + 16 + 49 = 116 \] 4. **Calculate the sample variance:** Since this is a sample, we divide by \( n-1 \) (degrees of freedom): \[ \text{Variance} = \frac{116}{7-1} = \frac{116}{6} \approx 19.33 \] Thus, the variance of the sample data set is approximately **19.33**.