In computing a measure of the central tendency for any set of 51 numbers, which one of the following measures is well-defined but uses only very few of the numbers of the set?

Options

A. Arithmetic mean
B. Geometric mean
C. Median
D. Mode

Explanation

To solve the question of which measure of central tendency is well-defined but uses only very few of the numbers in a set of 51 numbers, we can analyze the three common measures of central tendency: mean, median, and mode.

### Step-by-Step Solution:

1. **Understanding Measures of Central Tendency**:
- The three primary measures of central tendency are the mean, median, and mode.
- The mean is calculated by adding all the numbers in the set and dividing by the total count of numbers.
- The median is the middle value when all numbers are arranged in ascending or descending order.
- The mode is the value that appears most frequently in the dataset.

2. **Analyzing the Mean**:
- The mean requires all numbers in the dataset to be summed up, which means it uses all 51 numbers.
- Therefore, the mean is not the answer since it does not use only a few numbers.

3. **Analyzing the Median**:
- The median also requires all numbers to be arranged in order to find the middle value.
- As such, the median also uses all 51 numbers, making it not suitable for this question.

4. **Analyzing the Mode**:
- The mode is defined as the number that occurs most frequently in the dataset.
- To find the mode, we only need to identify the frequency of each number, which means we do not need to consider all numbers in the set.
- In many cases, especially when there are repeated values, we can determine the mode with just a few numbers.

5. **Conclusion**:
- Among the three measures, the mode is the only measure that is well-defined and can be determined using only a few of the numbers in the dataset.
- Thus, the answer to the question is the **mode**.