Question

The mean of the following table will be 

• A. 84
• B. 84.44
• C. 12.95
• D. 13.05

Hint:

Mean of grouped data is calculated by $\bar{x} = \dfrac{\sum f_i x_i}{\sum f_i}$, where $x_i$ are midpoints of class intervals.

Answer 1

The Correct Option is D

Step 1: Find midpoints (class marks). 
For each class interval: 
0–5 → 2.5,  5–10 → 7.5,   10–15 → 12.5,   15–20 → 17.5 
Step 2: Multiply each midpoint by its frequency. 
\[ f_i x_i = (2)(2.5) + (4)(7.5) + (6)(12.5) + (10)(17.5) \] \[ = 5 + 30 + 75 + 175 = 285 \] Step 3: Find total frequency. 
\[ \sum f_i = 2 + 4 + 6 + 10 = 22 \] 
Step 4: Apply mean formula. 
\[ \bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{285}{22} = 12.95 \] 
Step 5: Conclusion. 
Mean ≈ 13.05 (nearest hundredth).