# L6.Cummulative Frequency Histograms by Adela Sanders

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```									Name: ____________________________________                                   Date: __________________
Cumulative Frequency Histograms
Algebra 1

Exercise #1: Arlington High School gave a final exam to
all students taking Zoology. The total number of students              Interval
Frequency
taking this examination was 180. The test grades for these          (Test Scores)
students were grouped into a table below.                              51 - 60        15
61 - 70         30
(a) How many students scored “60 or less” on the test?                   71 - 80         55
81 - 90         50
91 - 100        30
(b) How many students scored “70 or less” on the test?

(c) How many students scored “80 or less” on the test?

(d) How many students scored “90 or less”                    (e) How many students scored “100 or less”
on the test?                                                 on the test?

The answers to the above questions are found by adding the “frequencies” from the intervals in the
table above. The histogram that displays these “accumulated” results is called a cumulative
frequency histogram.

Exercise #2: Fill in the cumulative frequency table given the frequency table below.

Interval                                         Interval         Cumulative
Frequency
(Test Scores)                                    (Test Scores)       Frequency
51 - 60                         15              51 - 60
61 - 70                         30              51 - 70
71 - 80                         55              51 - 80
81 - 90                         50              51 - 90
91 - 100                        30             51 - 100

Exercise #3: What must the last entry of the cumulative frequency table always be equal to? Explain.

Algebra 1, Unit # 10 – Statistics – L6
The Arlington Algebra Project, LaGrangeville, NY 12540
Exercise #4: The table below lists the heights of students, in inches, in Mr. Munson’s 2nd period class.

Interval                                     Interval           Cumulative
Frequency
(Student Heights)                            (Student Heights)       Frequency
50 - 54                           1           50-54
55 - 59                           3           50-59
60 - 64                           8           50-64
65 - 69                          12           50-69
70 - 74                           4           50-74

(a) Fill in the cumulative frequency table above.

(b) Construct a cumulative frequency histogram for this data set.

Exercise #5: A cumulative frequency table is given for the scores received on an Algebra 1 quiz.

(a) How many students took the quiz?                                                   Cumulative
Score Interval
Frequency
60 to 69                 3

(b) Students receive an A if they earned a 90% or better on         60 to 79                 8
the quiz. How many students received an A? Show                 60 to 89                20
60 to 99                29

Algebra 1, Unit # 10 – Statistics – L6
The Arlington Algebra Project, LaGrangeville, NY 12540
Name: ____________________________________                                    Date: __________________
Cumulative Frequency Histograms
Algebra 1 Homework
Applications
1. In the table below, the heights of 24 Varsity and Junior Varsity basketball players are given.

Heights                                    Heights          Cumulative
Frequency
(# of inches)                              (# of inches)       Frequency
71                           1           71
72                           2         71 - 72
73                           3         71 - 73
74                           6         71 - 74
75                           8         71 - 75
76                           2         71 - 76
77                           2         71 - 77

(a) Complete the cumulative frequency table above.

(b) What height represents the lower quartile?           (c) What height represents the upper quartile?

(d) Construct a cumulative frequency histogram on the grid below. Carefully label your axes.

Algebra 1, Unit # 10 – Statistics – L6
The Arlington Algebra Project, LaGrangeville, NY 12540
2. Traffic safety engineers sampled 80 speeds of cars driving along a road with a speed limit of 40
mph. Their results are given in the table below.
Cumulative
Speed Interval                Frequency              Speed Interval
Frequency
(mph)                     (no. of cars)              (mph)
(no. of cars)
25 to 29                         5                 25 to 29
30 to 34                        12                 25 to 34
35 to 39                        25                 25 to 39
40 to 44                        21                 25 to 44
45 to 49                         8                 25 to 49
50 to 54                         4                 25 to 54
(a) Fill out the cumulative frequency table above.

(b) What percent of drivers were traveling
below the speed limit?

(c) Construct a cumulative frequency histogram
on the grid to the right.

3. A survey of gasoline prices at New York gas stations showed the cumulative distribution below.

(a) How many gasoline stations were surveyed?                  Gas Price Interval        Cumulative
(In dollars per gallon)     Frequency
2.90 to 2.99               3
(b) How many gasoline stations are charging more than             2.90 to 3.09                5
\$3.19 per gallon? Show how your arrived at your