Understanding Cumulative Relative Frequency in Statistics: Calculation and Examples

Cumulative relative frequency

Cumulative relative frequency is a statistical concept that measures the proportion or percentage of data values that are less than or equal to a particular value in a dataset

Cumulative relative frequency is a statistical concept that measures the proportion or percentage of data values that are less than or equal to a particular value in a dataset. It provides a progressive tally of frequencies as data values increase.

To calculate the cumulative relative frequency, you need to follow these steps:

1. Organize the data set in ascending order from the smallest value to the largest value.

2. Calculate the cumulative frequency by adding up the frequencies of each data value as you progress through the dataset.

3. Calculate the relative frequency by dividing the frequency of each data value by the total number of observations in the dataset.

4. Calculate the cumulative relative frequency by adding up the relative frequencies as you progress through the dataset.

Let’s understand this concept with an example:

Suppose you have the following dataset of exam scores: 70, 80, 75, 90, 85, 80, 95, 75, 80, 85, 65.

1. Organize the data set in ascending order: 65, 70, 75, 75, 80, 80, 80, 85, 85, 90, 95.

2. Calculate the cumulative frequency:
– The first value is 65, and its frequency is 1.
– The second value is 70, and its frequency is 1 + 1 = 2.
– The third value is 75, and its frequency is 2 + 1 = 3.
– The fourth value is 75, and its frequency is 3 + 1 = 4.
– The fifth value is 80, and its frequency is 4 + 1 = 5.
– The sixth value is 80, and its frequency is 5 + 1 = 6.
– The seventh value is 80, and its frequency is 6 + 1 = 7.
– The eighth value is 85, and its frequency is 7 + 1 = 8.
– The ninth value is 85, and its frequency is 8 + 1 = 9.
– The tenth value is 90, and its frequency is 9 + 1 = 10.
– The eleventh value is 95, and its frequency is 10 + 1 = 11.

3. Calculate the relative frequency:
– The relative frequency of 65 is 1/11 ≈ 0.0909.
– The relative frequency of 70 is 2/11 ≈ 0.1818.
– The relative frequency of 75 is 4/11 ≈ 0.3636.
– The relative frequency of 80 is 7/11 ≈ 0.6364.
– The relative frequency of 85 is 9/11 ≈ 0.8182.
– The relative frequency of 90 is 10/11 ≈ 0.9091.
– The relative frequency of 95 is 11/11 = 1.

4. Calculate the cumulative relative frequency:
– The cumulative relative frequency of 65 is 0.0909.
– The cumulative relative frequency of 70 is 0.0909 + 0.1818 ≈ 0.2727.
– The cumulative relative frequency of 75 is 0.2727 + 0.3636 ≈ 0.6363.
– The cumulative relative frequency of 80 is 0.6363 + 0.6364 ≈ 1.2727.
– The cumulative relative frequency of 85 is 1.2727 + 0.8182 ≈ 2.0909.
– The cumulative relative frequency of 90 is 2.0909 + 0.9091 ≈ 3.
– The cumulative relative frequency of 95 is 3 + 1 = 4.

In summary, the cumulative relative frequencies corresponding to each unique value in the dataset are: 65 (0.0909), 70 (0.2727), 75 (0.6363), 80 (1.2727), 85 (2.0909), 90 (3), and 95 (4).

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