Question

The variance of the ungrouped data \(2, 12, 3, 11, 5, 10, 6, 7\) is:

• A. 11.875
• B. 11
• C. 12
• D. 10.765

Hint:

Variance is the average of squared deviations from the mean.

Answer 1

The Correct Option is C

Step 1: Calculate mean
\[ \bar{x} = \frac{2 + 12 + 3 + 11 + 5 + 10 + 6 + 7}{8} = \frac{56}{8} = 7 \] Step 2: Calculate squared deviations
\[ (2 - 7)^2 = 25, \quad (12 - 7)^2 = 25, \quad (3 - 7)^2 = 16, \quad (11 - 7)^2 = 16, \] \[ (5 - 7)^2 = 4, \quad (10 - 7)^2 = 9, \quad (6 - 7)^2 = 1, \quad (7 - 7)^2 = 0 \] Step 3: Calculate variance
\[ \sigma^2 = \frac{25 + 25 + 16 + 16 + 4 + 9 + 1 + 0}{8} = \frac{96}{8} = 12 \]