The marks scored by two students A and B in six subjects are given below:
`{:(A,71,56,45,89,54,44),(B,55,74,83,54,38,52):}`
Which one of the following statements is correct?

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 determine which statement is correct regarding the marks scored by students A and B, we will calculate the average scores for both students and analyze their consistency.

### Step 1: Calculate the Average Score of Student A
The marks scored by student A are: 71, 56, 45, 89, 54, and 44.

1. **Sum the marks of A:**
\[ 71 + 56 + 45 + 89 + 54 + 44 = 359 \]

2. **Count the number of subjects:**
There are 6 subjects.

3. **Calculate the average:**
\[ \text{Average of A} = \frac{359}{6} \approx 59.83 \]

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

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

2. **Count the number of subjects:**
There are 6 subjects.

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

### Step 3: Compare the Average Scores
- Average of A: 59.83
- Average of B: 59.33

Since the averages are not equal, we can conclude that the average scores of A and B are different.

### Step 4: Analyze Consistency
To analyze consistency, we will look at the variation in scores for both students.

1. **Calculate the range for A:**
- Maximum score: 89
- Minimum score: 44
- Range = 89 - 44 = 45

2. **Calculate the range for B:**
- Maximum score: 83
- Minimum score: 38
- Range = 83 - 38 = 45

3. **Standard deviation can also be used to analyze consistency, but based on the ranges, we can see that student B has less variation in scores.**

### Conclusion
Based on the calculations:
- The average scores of A and B are not the same.
- Student B shows more consistency in their scores compared to student A.

Thus, the correct statement is that "the average scores of A and B are not the same, but B is more consistent."