Cumulative Frequency Tables & Histograms:
You are probably familiar with the word cumulative. Cumulative means the total of all
frequencies. Cumulative totals can be used to determine how many scores are above or
below a set level. Cumulative frequency tables are easy to construct once we have made
the basic frequency table.
Example:
Class Boundaries
Tally
18.5 – 22.5
22.5 – 26.5
26.5 – 30.5
30.5 – 34.5
34.5 – 38.5
Frequency
7
9
6
10
3
Cumulative
Frequency
7
16
22
32
35
Notice, the only column that we had to add was the cumulative frequency column. Then,
all we have to do is add up the frequencies as we go from class to class and write down
the total. The cumulative frequency for a class is the sum of the frequencies for that class
and all the previous classes.
After we have completed the frequency table, at this point in the course we should know
how to construct a histogram. However, if we are asked to construct a cumulative
frequency histogram, then we will use the data from the last column. We will then see
the bars of our histogram increase as we go from left to right, with the possibility that
some of the bars may stay the same height.
For each of the following, construct a cumulative frequency table and a cumulative
frequency histogram:
1) In a school, a final examination was given to all students taking biology. The
total number of students taking this examination was 24. The test grades of
these students are shown below:
99
100
84
86
72
88
100
76
54
88
77
77
91
90
88
54
59
72
99
77
86
88
88
89
Hint: Use five classes!
a)
b)
c)
d)
e)
How many students scored 60 or less on the test?
How many students scored 70 or less on the test?
How many students scored 80 or less on the test?
How many students scored 90 or less on the test?
How many students scored 100 or less on the test?
2) 20 players were selected to play on the varsity. The heights in inches of these
players is as follows:
75
77
76
71
73
73
72
75
75
72
77
75
75
75
74
74
74
74
74
75
Hint: Use seven classes!
3) A random sample of 42 auto insurance claims made on All State Insurance
Company gave the following information to the nearest dollar:
705
800
1090 2408 2010 910
350
690
520
750
1000
860
170
1100 1150 1590 1841 1880 1942 2210 1886 1954
1710 1372 1200 1210 1351 1400 1790 1682 1310 1460 1550
1300 1463 1511 1190 1200 2350 510
1285 1700
Hint: Use eight classes!
4) 18 students sold the following amount of raffle tickets for the school fundraiser:
80 80
95
90
90
85
83
97
86
86
80
94 100
80
100
98
96
91
Hint: Use 6 classes!
5) The following represents the daily temperatures in Orlando during the month
of September:
65 67
68
75
77
77
79
82
83
84
84
85 85
86
88
88
90
90
92
93
93
94
95 97
99
Hint: Use 4 classes!