Question

What is the variance of the following data? \( 9, 10, 13, 14, 6, 11, 8, 7, 4, 18 \)

• A. 12
• B. 13.6
• C. 14
• D. 15.6

Hint:

When calculating variance, first find the mean of the data, then calculate the squared differences from the mean.

Answer 1

The Correct Option is B

The variance is given by: \[ \text{Variance} = \frac{\sum (x_i - \mu)^2}{n} \] Where \( \mu \) is the mean and \( x_i \) are the data points. Calculate the mean: \[ \mu = \frac{9 + 10 + 13 + 14 + 6 + 11 + 8 + 7 + 4 + 18}{10} = 9.9 \] Then calculate the squared deviations and the average squared deviation: \[ \text{Variance} = \frac{(9 - 9.9)^2 + (10 - 9.9)^2 + \dots + (18 - 9.9)^2}{10} = 13.6 \]