1. Frequency and Histograms
10-2
Frequency and Histograms
Holt Algebra 1

2. Objectives
Create frequency tables and histograms.

3. Vocabulary interval frequency frequency table histogram
cumulative frequency

4. interval: the numbers between two specific values
interval size: a count of the two specific values in an interval and the numbers between them

5. Interval Interval Size 36 - 38 0 - 5 10 - 19 1 - 7
State the size of each interval.
Interval
Interval Size
0 - 5
1 - 7 3 6 10 7
How do you determine the size of an interval?
Subtract the 2 numbers in the interval and add 1.

6. Creating equal intervals
Create equal intervals of the data.
The final scores for each golfer in a tournament
77, 71, 70, 82, 75, 76, 72, 70, 77, 74, 71, 75, 68,
72, 75, 74
Step 1 Identify the least and greatest values in a set of data.
68 and 82
Step 2 Decide on the the size of the intervals.
(Typically, you want intervals in the table with interval sizes of 2 or higher)
Step 3 Create intervals that have the same size.

7. The frequency of a data value is the number of times it occurs.
A frequency table shows the frequency of each data value.

8. Golf Tournament Scores
Example 1: Making a Frequency Table
Use the golf score data to make a frequency table with intervals. Make the first interval
77, 71, 70, 82, 75, 76, 72, 70, 77, 74, 71, 75, 68, 72, 75, 74
Golf Tournament Scores
Scores
Frequency
68 – 71 5
72 – 75 7
76 – 79 3
80 – 83 1

9. Number of Vacation Days
Example 2
The number of days of Maria’s last 15 vacations are listed below. Use the data to make a frequency table with intervals of 3.
4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12
Number of Vacation Days
Interval
Frequency
4 – 6 5
7 – 9 4
10 – 12
13 – 15 2

10. Vowels in Sentences 28-31 2 32-35 7 9 36-39 5 14 40-43 3 17
Cumulative frequency shows the frequency of all data values less than or equal to a given value.
Vowels in Sentences
Number
Frequency
Cumulative
28-31 2
32-35 7 9
36-39 5 14
40-43 3 17

11. A histogram is a special bar graph where the bars touch.
The bars must be of equal width and should touch, but not overlap.

12. Example 3: Making a Histogram
Make a histogram for the number of days of Maria’s last 15 vacations. Use intervals of 3.
4, 8, 6, 7, 5, 4, 10, 6, 7, 14, 12, 8, 10, 15, 12
Step 1 Choose intervals for the horizontal axis. The intervals must be the same size.
Step 2 Draw a bar for the number of scores in each interval.
Step 3 Title the graph and label the horizontal and vertical axes.

13. Example 3 Continued
Vacations

14. Example 4
The number of miles on the new cars in a car lot are given below.
35, 21, 15, 51, 39, 41, 46, 22, 28, 16, 12, 40, 34, 56, 25, 14, 20, 35, 30
Use the data to make a histogram.

15. Example 5: Making a Cumulative Frequency Table
The weights (in ounces) of packages of beef patties are given below.
19, 20, 26, 18, 25, 29, 18, 18, 22, 24, 27, 26, 24, 21, 29, 19
a. Use the data to make a cumulative frequency table.
Step 1 Make a frequency table with intervals.
Step 2 Add a “cumulative frequency” column to the table.

16. Example 5 Continued
Step 3 Add the frequency of each interval to the frequencies of all the intervals before it.
Step 4 Title the table.
Beef Patties
Weight (oz)
Frequency
Cumulative
18-20 6
21-23 2 8
24-26 5 13
27-29 3 16

17. b. How many packages weigh less than 24 ounces?
Example 5 Continued
b. How many packages weigh less than 24 ounces?
There are 8 packages with weights under 24 oz.
Beef Patties
Weight (oz)
Frequency
Cumulative
18-20 6
21-23 2 8
24-26 5 13
27-29 3 16

18. Example 6
The number of vowels in each sentence of a short essay are listed below.
33, 36, 39, 37, 34, 35, 43, 35, 28, 32, 36, 35, 29, 40, 33, 41, 37
a. Use the data to make a cumulative frequency table.
Step 1 Choose intervals for the first column of the table.
Step 2 Record the frequency values in each interval for the second column.

19. Vowels in Sentences 28-31 2 32-35 7 9 36-39 5 14 40-43 3 17
Example 6 Continued
Step 3 Add the frequency of each interval to the frequencies of all the intervals before it. Put that number in the third column of the table.
Vowels in Sentences
Step 4 Title the table.
Number
Frequency
Cumulative
28-31 2
32-35 7 9
36-39 5 14
40-43 3 17

20. Vowels in Sentences 28-31 2 32-35 7 9 36-39 5 14 40-43 3 17
Example 6 Continued
b. How many sentences contain 35 vowels or fewer?
All sentences with less than 35 vowels. are displayed in the first two rows of the table, so look at the cumulative frequency shown in the second row.
Vowels in Sentences
Number
Frequency
Cumulative
28-31 2
32-35 7 9
36-39 5 14
40-43 3 17
There are 9 sentences with fewer than 35 vowels.