The running total
Add each class's frequency to everything before it.
How many scored less than 20?
53 students took a test out of 100. The table shows how many scored in each class. In the class 0–10 there are 5 students, and in 10–20 there are 3.
We want to know how many students scored less than 20.
How many students scored less than 20?
What this lesson covers
The idea
The cumulative frequency of a class is the running total of the frequencies up to and including that class, so it counts the observations below the class's upper limit; these totals form the cumulative frequency column.
How many scored less than 20?
53 students took a test out of 100. The table shows how many scored in each class. In the class 0–10 there are 5 students, and in 10–20 there are 3.
We want to know how many students scored less than 20.
How many students scored less than 20?
- 3, the students in 10–20
- 5, the students in 0–10
- 8, both classes together
Add down the table
Tap the highlighted cell in each row. It adds the frequency of the class to the total of all the classes before it. The blue bar grows with the total. Go all the way down.
Cumulative frequency
The cumulative frequency of a class is the frequency of the class plus the frequencies of all the classes before it. It counts the observations below the class's upper limit.
The cumulative frequency of 10–20 is 5 + 3 = 8: eight students scored less than 20. The last cumulative frequency is the total number of observations, 53. The column of these totals is the cumulative frequency column.
Notes
The cumulative frequency of a class is the running total of the frequencies up to and including that class. It counts the observations below the upper limit.
Check yourself
Using the table of the 53 students (frequencies 5, 3, 4, 3, 3, 4, 7, 9, 7, 8), find the cumulative frequency of the class 40–50.
Answer: 18
5 + 3 + 4 + 3 + 3 = 18. Eighteen students scored less than 50.
How many of the 53 students scored less than 70?
Answer: 29
5 + 3 + 4 + 3 + 3 + 4 + 7 = 29.
The 30 students grouped in Table 13.3 have frequencies 2, 3, 7, 6, 6, 6 in the classes 10–25, 25–40, 40–55, 55–70, 70–85, 85–100. Find the cumulative frequency of 55–70.
Answer: 18
2 + 3 + 7 + 6 = 18. Eighteen students scored less than 70.
Using the cumulative frequencies of the 53 students (…, 22 less than 60, 29 less than 70, 38 less than 80), how many students scored from 60 up to less than 80?
Answer: 16
38 − 22 = 16. (The classes 60–70 and 70–80 have 7 + 9 = 16 students.)