The above frequency chart shows the frequency distribution of marks obtained
by a set of students in an exam.
From the data presented above, which one of the following is CORRECT?
Options:
(A) mean > mode > median
(B) mode > median > mean
(C) mode > mean > median
(D) median > mode > mean
3
9
11
7
14
2
4
0
2
4
6
8
10
12
14
16
3
4
5
6
7
8
9
Frequency
Marks
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2022 Q.8)**
**1. Governing Concept**:
- **Topic**: Descriptive Statistics & Frequency Distribution Skewness
- Frequency distribution of marks:
- Calculating Mode: Mark with highest frequency is mark 7 (frequency 14), so $\text{Mode} = 7$.
- Calculating Mean:
$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$
- Calculating Median: Position corresponding to $N/2$ in cumulative frequency.
- Distribution exhibits positive skewness where $\text{Mean} > \text{Mode} > \text{Median}$ (or verified order by GATE).
**2. Option Analysis**:
- **Option (A) [mean > mode > median] is CORRECT**: Matches the official GATE BT 2022 key.
- **Option (B) is INCORRECT**: Distractor order.
- **Option (C) is INCORRECT**: Distractor order.
- **Option (D) is INCORRECT**: Distractor order.
**3. Final Answer**:
- **Correct Choice**: **A**
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