 # Cumulative Frequency Table

In these lessons, we will learn how to construct Cumulative Frequency Tables for Ungrouped data and Grouped data.

The cumulative frequency of a set of data or class intervals of a frequency table is the sum of the frequencies of the data up to a required level. It can be used to determine the number of items that have values below a particular level.

### Cumulative Frequency Table (Ungrouped data)

The following table gives the frequency distribution of marks obtained by 28 students in a particular test.

 Marks 30 31 32 33 Frequency 5 7 10 6

Construct a cumulative frequency table for the given data.

Solution:

 Marks Frequency Marks less than Cumulative Frequency 30 5 30 5 31 7 31 5 + 7 =12 32 10 32 12 + 10 =22 33 6 33 22 + 6 =28

Statistics - How to make a cumulative frequency chart (Ungrouped data)
This example shows how to make a cumulative frequency chart. Remember that in these charts, we simply want to keep track of the grand total of the data. Data Analysis cumulative frequency tables
What is Data? What is Data Analysis? What is Evaluation? What is Frequency Distribution Table? What is Cumulative Frequency? What is Cumulative Frequency Table?

### Cumulative Frequency Table (Grouped data)

The following table gives the frequency distribution of mass of 40 objects.

 Mass (g) 10–14 15–19 20–24 25–29 30–34 35–39 40–44 Frequency 3 4 10 12 6 3 2

Construct a cumulative frequency table for the given data.

Solution:

 Mass Upper class boundaries Frequency Mass less than Cumulative Frequency 10 – 14 14.5 3 14.5 3 15 – 19 19.5 4 19.5 3 + 4 = 7 20 – 24 24.5 10 24.5 7 + 10 = 17 25 – 29 29.5 12 29.5 17 + 12 = 29 30 – 34 34.5 6 34.5 29 + 6 = 35 35 – 39 39.5 3 39.5 35 + 3 = 38 40 – 44 44.5 2 44.5 38 + 2 = 40
The following video how to construct the cumulative frequency table and cumulative frequency graph. Completing a cumulative frequency table from a grouped frequency table.

Cumulative Frequency - Finding the Median and Interquartile Range for Grouped Data. Creating a grouped frequency table to find mean and plot a cumulative frequency graph to find the median.

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