The cumulative frequency of the largest observed value must always be :

Options

A. Less than the total number of observations
B. Greater than the total number of observation
C. Equal to total number of observation
D. Equal to mid point of the last class interval

Explanation

To solve the question regarding the cumulative frequency of the largest observed value, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Cumulative Frequency**:
Cumulative frequency is the running total of frequencies up to a certain point in a dataset. It helps in understanding how many observations fall below a particular value.

2. **Identify the Largest Observed Value**:
The largest observed value in a dataset is the maximum value that has been recorded.

3. **Calculate Cumulative Frequency**:
To find the cumulative frequency for each value in a dataset, we start with the first frequency and keep adding subsequent frequencies. The cumulative frequency for the largest observed value will be the total of all frequencies.

4. **Summation of Frequencies**:
If we denote the frequencies as \( f_1, f_2, f_3, \ldots, f_n \), the cumulative frequency for the largest observed value (let's denote it as \( CF_{\text{max}} \)) can be calculated as:
\[ CF_{\text{max}} = f_1 + f_2 + f_3 + \ldots + f_n \]

5. **Conclusion**:
The cumulative frequency of the largest observed value must always equal the total number of observations in the dataset. Therefore, we can conclude:
\[ CF_{\text{max}} = \text{Total Number of Observations} \]

### Final Answer:
The cumulative frequency of the largest observed value must always be equal to the total number of observations.

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