In the following distribution, mean is : 3 4 5 6 7 8 9 10 : 2 4 2 3 5 4 3 7

The correct answer is C. This is a frequency distribution, so the mean is the weighted mean: sum of (x × f) divided by sum of f.

• Products x×f: 3×2=6, 4×4=16, 5×2=10, 6×3=18, 7×5=35, 8×4=32, 9×3=27, 10×7=70.
• Sum of products = 214; total frequency = 30.
• Mean = 214/30 = 7.13, which rounds to 7.1.

Why the others fail: Option A (10) is just the largest value in the data, and the mean cannot equal it when most observations are smaller. Option B (7) is the mode, since 7 has the highest frequency (5), not the mean. Option D (6.5) is the simple average of the distinct values (52/8), which ignores the frequencies entirely.

Core concept: arithmetic mean of frequency data, a basic statistics tool used in data interpretation and in Mains answers on census and survey figures.

Trap: Averaging the listed values without weighting them by frequency, which gives 6.5.