Question

Variance of 240, 260, 270, 280

• A. 15
• B. 16
• C. 18
• D. 20

Hint:

Variance measures the spread of a data set around the mean. A higher variance indicates greater variability.

Answer 1

The Correct Option is B

To find the variance, we first calculate the mean (\(\mu\)) of the given data: \[ \mu = \frac{240 + 260 + 270 + 280}{4} = 262.5 \] Next, we calculate the squared differences from the mean for each data point: \[ (240 - 262.5)^2 = 506.25, \quad (260 - 262.5)^2 = 6.25, \quad (270 - 262.5)^2 = 56.25, \quad (280 - 262.5)^2 = 306.25 \] Finally, the variance is the average of these squared differences: \[ \text{Variance} = \frac{506.25 + 6.25 + 56.25 + 306.25}{4} = 16 \]