$\begin{array}{c|c} Class Interval & 3 - 5 & 6 - 8 & 9 - 11 \\ \hline Frequency & 2 & 2 & 2 \end{array}$. Find the standard deviation of the above distribution.

Analyze the question: We have a grouped frequency distribution and must find its standard deviation. We use the class midpoints.

Concept: For grouped data, σ = √[Σf(x − x̄)² / Σf]

Step 1: Midpoints

• 3–5 → x = 4
• 6–8 → x = 7
• 9–11 → x = 10

Step 2: Mean Σf = 6 Σfx = 2(4) + 2(7) + 2(10) = 8 + 14 + 20 = 42 x̄ = 42/6 = 7

Step 3: Deviations

• x = 4: d = −3, d² = 9, fd² = 18
• x = 7: d = 0, d² = 0, fd² = 0
• x = 10: d = 3, d² = 9, fd² = 18

Σfd² = 36

Step 4: Standard deviation σ = √(36/6) = √6

(Note: if you used the sample formula dividing by n − 1 = 5, you'd get √(36/5), which is not among the options. JAMB uses the population formula dividing by Σf.)

Answer: B. √6

Tip: Always use the class midpoints for grouped data. When the frequencies are equal and the midpoints are evenly spaced, the mean is simply the middle midpoint, which makes the deviations quick to find.