# Cumulative Relative Frequency

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Cumulative relative frequency refers to the proportion of data values that are less than or equal to a certain value. It is usually expressed in the form of a percentage.

For example, suppose that in a test of 100 marks the cumulative frequency for 60 marks is 85%. This means that 85% of the students have obtained less than 60 marks in the exam.

The cumulative relative frequency can be represented easily in the form of a cumulative relative frequency table.

### How do you find the cumulative relative frequency?

1. Represent the data in the form of a frequency distribution table.
2. Find the cumulative frequencies by summing up the frequencies of the current and the preceding class intervals.
3. Divide the cumulative frequencies by the total frequency. This gives us the cumulative relative frequency.
4. If needed, we convert the cumulative relative frequencies obtained above into percentages by multiplying the proportion by 100.

### Example:

Consider the following data given in the form of a frequency table.

We find out the cumulative relative frequency table as follows.

Step 1: We find out the cumulative frequency by adding up the frequencies of the current and previous class intervals.

Step 2: We find out the relative cumulative frequency by dividing the cumulative frequency by the total frequency.

Step 3: We convert the relative cumulative frequency into percentages by multiplying it by 100

### Remarks:

1. The cumulative relative frequency for the last class must always be 1 because we are dividing the total frequency by itself to calculate the final cumulative relative frequency.

2. A cumulative relative frequency distribution shows us the percentage of data values that lie below an upper class interval.

3. A cumulative relative frequency graph or a cumulative frequency histogram is drawn in the usual way except for the fact that we plot the cumulative relative frequencies on the Y axis.

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