Understanding Cumulative Relative Frequency: A Step-by-Step Guide

Cumulative relative frequency

Cumulative relative frequency is a statistical concept that measures the proportion or percentage of data points that are less than or equal to a given value in a data set

Cumulative relative frequency is a statistical concept that measures the proportion or percentage of data points that are less than or equal to a given value in a data set.

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

Step 1: Organize your data set in ascending order (from lowest to highest).

Step 2: For each data point, calculate the relative frequency, which is the number of occurrences of that value divided by the total number of data points in your set.

Step 3: Calculate the cumulative frequency. To do this, add up the relative frequencies from the smallest value in your data set up to the current value.

Step 4: Calculate the cumulative relative frequency. This is done by dividing the cumulative frequency by the total number of data points in your set.

Let’s understand this concept with an example:

Consider the following data set: 7, 12, 9, 4, 17

Step 1: Organize the data in ascending order: 4, 7, 9, 12, 17

Step 2: Calculate the relative frequency for each data point:

– 4 appears once, so its relative frequency is 1/5 = 0.2 (20%).
– 7 appears once, so its relative frequency is also 1/5 = 0.2 (20%).
– 9 appears once, so its relative frequency is 1/5 = 0.2 (20%).
– 12 appears once, so its relative frequency is 1/5 = 0.2 (20%).
– 17 appears once, so its relative frequency is 1/5 = 0.2 (20%).

Step 3: Calculate the cumulative frequency:

– For 4, the cumulative frequency is 0.2 (20%).
– For 7, the cumulative frequency is 0.2 + 0.2 = 0.4 (40%).
– For 9, the cumulative frequency is 0.2 + 0.2 + 0.2 = 0.6 (60%).
– For 12, the cumulative frequency is 0.2 + 0.2 + 0.2 + 0.2 = 0.8 (80%).
– For 17, the cumulative frequency is 0.2 + 0.2 + 0.2 + 0.2 + 0.2 = 1 (100%).

Step 4: Calculate the cumulative relative frequency:

– For 4, the cumulative relative frequency is 0.2 (20%).
– For 7, the cumulative relative frequency is 0.4 (40%).
– For 9, the cumulative relative frequency is 0.6 (60%).
– For 12, the cumulative relative frequency is 0.8 (80%).
– For 17, the cumulative relative frequency is 1 (100%).

The cumulative relative frequency provides insights into the distribution of the data set and allows you to make comparisons between different values or groups. It is particularly useful in analyzing cumulative distributions and cumulative frequency histograms.

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