Which one of the following measures is determined only after the construction of cumulative frequency distribution

Options

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

Answer

To solve the question, we need to determine which measure is calculated only after constructing a cumulative frequency distribution. The options provided are:

A) Arithmetic Mean
B) Mode
C) Median
D) Geometric Mean

### Step-by-Step Solution:

1. **Understanding the Measures**:
- **Arithmetic Mean**: This is calculated by summing all values in a dataset and dividing by the number of values. It does not require a cumulative frequency distribution.
- **Mode**: This is the value that appears most frequently in a dataset. It can be determined directly from the data without needing cumulative frequency.
- **Geometric Mean**: This is calculated using the formula \( \sqrt[n]{x_1 \times x_2 \times \ldots \times x_n} \). Like the mean and mode, it does not require cumulative frequency.
- **Median**: This is the middle value of a dataset when it is ordered. To find the median in grouped data, we use the cumulative frequency distribution.

2. **Identifying the Correct Answer**:
- The median is the only measure that requires the construction of a cumulative frequency distribution to be calculated accurately in grouped data. Therefore, the correct answer is **C) Median**.

3. **Conclusion**:
- After analyzing the definitions and calculation methods for each measure, we conclude that the median is the only measure that is determined after constructing a cumulative frequency distribution.

### Final Answer:
C) Median