10-2Frequency
10-2
Frequencyand
andHistograms
Histograms
Holt
Algebra
Holt
Algebra
11
10-2 Frequency and Histograms
Objectives
Create frequency tables and
histograms.
Holt Algebra 1
10-2 Frequency and Histograms
Vocabulary
interval
frequency
frequency table
histogram
cumulative frequency
Holt Algebra 1
10-2 Frequency and Histograms
interval: the numbers between two specific
values
interval size: a count of the two specific values
in an interval and the numbers between them
Holt Algebra 1
10-2 Frequency and Histograms
State the size of each interval.
Interval Interval Size
3
36 - 38
0-5
10 - 19
1-7
6
10
7
How do you determine the size of an interval?
Subtract the 2 numbers in the interval and add 1.
Holt Algebra 1
10-2 Frequency and Histograms
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 4 - 7 intervals in the table with
interval sizes of 2 or higher)
Step 3 Create intervals that have the same size.
Holt Algebra 1
10-2 Frequency and Histograms
The frequency of a data value is the number of
times it occurs.
A frequency table shows the frequency of each
data value.
Holt Algebra 1
10-2 Frequency and Histograms
Example 1: Making a Frequency Table
Use the golf score data to make a frequency table
with intervals. Make the first interval 68 - 71.
77, 71, 70, 82, 75, 76, 72, 70, 77, 74, 71, 75,
68, 72, 75, 74
Golf Tournament Scores
Holt Algebra 1
Scores
Frequency
68 – 71
72 – 75
76 – 79
5
7
3
80 – 83
1
10-2 Frequency and Histograms
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
Holt Algebra 1
Interval
Frequency
4–6
7–9
5
4
10 – 12
13 – 15
4
2
10-2 Frequency and Histograms
Cumulative frequency shows the frequency of
all data values less than or equal to a given
value.
Vowels in Sentences
Holt Algebra 1
Number
Frequency
Cumulative
Frequency
28-31
2
2
32-35
7
9
36-39
5
14
40-43
3
17
10-2 Frequency and Histograms
A histogram is a special bar graph where
the bars touch.
The bars must be of equal width and should
touch, but not overlap.
Holt Algebra 1
10-2 Frequency and Histograms
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.
Holt Algebra 1
10-2 Frequency and Histograms
Example 3 Continued
Vacations
Holt Algebra 1
10-2 Frequency and Histograms
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.
Holt Algebra 1
10-2 Frequency and Histograms
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.
Holt Algebra 1
10-2 Frequency and Histograms
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.
Holt Algebra 1
Beef Patties
Weight
(oz)
Frequency
Cumulative
Frequency
18-20
6
6
21-23
2
8
24-26
5
13
27-29
3
16
10-2 Frequency and Histograms
Example 5 Continued
b. How many packages weigh less than 24 ounces?
There are 8 packages with weights under 24 oz.
Beef Patties
Holt Algebra 1
Weight
(oz)
Frequency
Cumulative
Frequency
18-20
6
6
21-23
2
8
24-26
5
13
27-29
3
16
10-2 Frequency and Histograms
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.
Holt Algebra 1
10-2 Frequency and Histograms
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.
Step 4 Title the
table.
Holt Algebra 1
Vowels in Sentences
Number
Frequency
Cumulative
Frequency
28-31
2
2
32-35
7
9
36-39
5
14
40-43
3
17
10-2 Frequency and Histograms
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.
There are 9 sentences
with fewer than 35
vowels.
Holt Algebra 1
Vowels in Sentences
Number
Frequency
Cumulative
Frequency
28-31
2
2
32-35
7
9
36-39
5
14
40-43
3
17