We want to use the frequency table of a data set to make a cumulative frequency table. Recall that a frequency table splits the data values into intervals and shows the frequency for each interval. Let's take a look at an example frequency table that represents the number of 3-point shots made in the games played by our school's basketball team.
Number of 3-Point Shots
Frequency
0-1
13
2-3
2
4-5
3
6-7
1
Now we will use this table to construct a cumulative frequency table. A cumulative frequency table shows the number of data values that lie in or below a particular interval. Therefore, we will add the frequencies of all of the previous intervals to the frequency of each interval. Let's write the sum in a third column.
Number of 3-Point Shots
Frequency
Cumulative Frequency
0-1
13
13
2-3
2
13 + 2 = 15
4-5
3
13 + 2 + 3 = 18
6-7
1
13 + 2 + 3 + 1 = 19
Finally, we can conclude how to use a frequency table to make a cumulative frequency table.
Add the frequencies of all the previous intervals to the frequency of each interval.
Alternative Solution
Different Method of Constructing a Cumulative Frequency Table
We can also construct the cumulative frequency table by adding the previous cumulative frequency to the frequency of each interval. For the first cumulative frequency, write only the frequency of the first interval.
Number of 3-point Goals
Frequency
Cumulative Frequency
0-1
13
13
2-3
2
13 + 2 = 15
4-5
3
15+ 3 = 18
6-7
1
18 + 1 = 19
Note that we obtained exactly the same result as when using the previous method.
