Question

Calculate the variance of the data set: 1, 2, 3, 5, 8, 13, 17.

• A. 31.14
• B. 29.57
• C. 30.62
• D. 32.71

Hint:

Variance measures the spread of a data set relative to its mean and is calculated as the average of the squared differences from the Mean.

Answer 1

The Correct Option is A

First, calculate the mean of the data: \[ \text{Mean} = \frac{1 + 2 + 3 + 5 + 8 + 13 + 17}{7} = \frac{49}{7} = 7 \] Next, compute the sum of the squared differences from the mean: \[ \text{Sum of squares} = (1-7)^2 + (2-7)^2 + (3-7)^2 + (5-7)^2 + (8-7)^2 + (13-7)^2 + (17-7)^2 \] \[ = 36 + 25 + 16 + 4 + 1 + 36 + 100 = 218 \] Finally, the variance (\(\sigma^2\)) is calculated as: \[ \sigma^2 = \frac{\text{Sum of squares}}{n} = \frac{218}{7} \approx 31.14 \]