Question

Find the variance of the following frequency distribution:

Class Interval
	0--4	4--8	8--12	12--16
Frequency	1	2	2	1

• A. 16
• B. \( \frac{44}{3} \)
• C. 23
• D. \( \frac{22}{3} \)

Hint:

Use midpoints for class intervals and apply variance formula \( \sigma^2 = \frac{\sum f(x - \bar{x})^2}{\sum f} \)

Answer 1

The Correct Option is B

Find midpoints: 2, 6, 10, 14 \[ \text{Mean: } \bar{x} = \frac{1\cdot2 + 2\cdot6 + 2\cdot10 + 1\cdot14}{6} = \frac{58}{6} = \frac{29}{3} \] Now compute variance: \[ \sigma^2 = \frac{1}{6}[(2 - \frac{29}{3})^2 + 2(6 - \frac{29}{3})^2 + 2(10 - \frac{29}{3})^2 + (14 - \frac{29}{3})^2] = \frac{44}{3} \]