L6.Cummulative Frequency Histograms by Adela Sanders

VIEWS: 0 PAGES: 4

									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
    how you arrive at your answer.
                                                                    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
    answer.                                                       2.90 to 3.19                15
                                                                  2.90 to 3.29                22
                                                                  2.90 to 3.39                32
(c) What percent of gasoline stations charged less than $3.10 per gallon?


Algebra 1, Unit # 10 – Statistics – L6
The Arlington Algebra Project, LaGrangeville, NY 12540

								
To top