The marks scored by two students A and B is six subjects are given below
`{:(A,71,56,55,75,54,49),(B,55,74,83,54,38,52):}`
Which one of the following statements is most appropriate?

Options

A. The average scores of A and B are same but A is consistent
B. The average scores of A and B are not same but A is consistent
C. The average scores of A and B are same but B is consistent
D. The average scores of A and B are same but B is consistent

Explanation

To solve the problem, we need to calculate the average marks of students A and B and analyze their consistency based on the marks provided.

### Step 1: Calculate the average marks of student A
The marks scored by student A are: 71, 56, 55, 75, 54, 49.

1. **Sum the marks of A**:
\[ 71 + 56 + 55 + 75 + 54 + 49 = 360 \]

2. **Number of subjects**: 6

3. **Calculate the average**:
\[ \text{Average of A} = \frac{\text{Sum of marks}}{\text{Number of subjects}} = \frac{360}{6} = 60 \]

### Step 2: Calculate the average marks of student B
The marks scored by student B are: 55, 74, 83, 54, 38, 52.

1. **Sum the marks of B**:
\[ 55 + 74 + 83 + 54 + 38 + 52 = 356 \]

2. **Number of subjects**: 6

3. **Calculate the average**:
\[ \text{Average of B} = \frac{\text{Sum of marks}}{\text{Number of subjects}} = \frac{356}{6} \approx 59.33 \]

### Step 3: Compare the average marks
- Average of A = 60
- Average of B ≈ 59.33

From this calculation, we can see that:
- The average marks of A (60) is higher than the average marks of B (approximately 59.33).

### Step 4: Analyze the consistency of marks
To determine which student is more consistent, we can look at the variation in their scores.

1. **Calculate the range of marks for A**:
- Highest mark = 75
- Lowest mark = 49
- Range = 75 - 49 = 26

2. **Calculate the range of marks for B**:
- Highest mark = 83
- Lowest mark = 38
- Range = 83 - 38 = 45

Since the range of marks for student A (26) is less than that of student B (45), student A is more consistent.

### Conclusion
- Average marks of A > Average marks of B
- Student A is more consistent than student B.

### Final Answer
The most appropriate statement is that student A has a higher average score and is more consistent than student B.

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