Transcript Sec. 10

10-2 Frequency and Histograms
A measure of central tendency describes the
center of a set of data. Measures of central
tendency include the mean, median, and mode.
• The mean is the average of the data values,
or the sum of the values in the set divided by
the number of values in the set.
• The median the middle value when the values
are in numerical order, or the mean of the two
middle numbers if there are an even number of
values.
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10-2 Frequency and Histograms
• The mode is the value or values that occur
most often. A data set may have one mode or
more than one mode. If no value occurs more
often than another, we say the data set has no
mode.
The range of a set of data is the difference
between the least and greatest values in the
set. The range describes the spread of the data.
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Additional Example 1: Finding Mean, Median, Mode,
and Range of a Data Set
The weights in pounds of six members of a
basketball team are 161, 156, 150, 156, 150,
and 163. Find the mean, median, mode, and
range of the data set.
Write the data in numerical
Add all the values and divide
order.
by the number of values.
mean:
median: 150, 150, 156, 156, 161, 163
The median is 156.
There are an even number of values. Find the mean of the two
middle values.
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10-2 Frequency and Histograms
Additional Example 1 Continued
150, 150, 156, 156, 161, 163
modes: 150 and 156
range: 163 – 150 = 13
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150 and 156 both occur
more often than any other
value.
10-2 Frequency and Histograms
Check It Out! Example 1
The weights in pounds of five cats are 12, 14,
12, 16, and 16. Find the mean, median, mode,
and range of the data set.
12, 12, 14, 16, 16
Write the data in numerical
order.
Add all the values and divide
by the number of values.
median: 12, 12, 14, 16, 16
The median is 14.
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There are an odd number of
values. Find the middle
value.
10-2 Frequency and Histograms
Check It Out! Example 1 Continued
The weights in pounds of five cats are 12, 14,
12, 16, and 16.Find the mean, median, mode,
and range of the data set.
mode: 12 and 16
range: 12 – 16 = 4
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The data set is bi-modal as
12 and 14 both occur
twice.
10-2 Frequency and Histograms
A stem-and-leaf plot arranges data by dividing
each data value into two parts. This allows you
to see each data value.
The digits other than
the last digit of each
value are called a
stem.
The last digit of a
value is called a leaf.
Key: 2|3 means 23
The key tells you how
to read each value.
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Example 2A: Reading a Stem-and-Leaf Plot
The stem-and-leaf plot below shows the
numbers of defective widgets in batches of
1000 are given below. Use the stem-and-leaf
plot to answer the following questions.
Number of Defective
Widgets per Batch
Stem Leaves
0 8899
1 233459
2 01
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Example 2A: Reading a Stem-and-Leaf Plot
Number of Defective
Widgets per Batch
Stem Leaves
0
1
2
8899
233459
01
A. What is the median number of defective
widgets per batch?
B. What is the mean number of defective widgets
per batch?
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Example 2A: Reading a Stem-and-Leaf Plot
Number of Defective
Widgets per Batch
Stem Leaves
0
1
2
8899
233459
01
C. How many orders had less than 15 defective
widgets?
D. About what percent of the batches had fewer
than 10 defective widgets?
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Example 2B Reading a Stem-and-Leaf Plot
The season’s scores for the football teams
going to the state championship are given in
the stem-and-leaf plot below. Use the data to
answer the following questions
Football State
Championship Scores
Team A
3
9522 4
865 5
51 6
2 7
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Team B
7
889
278
013
10-2 Frequency and Histograms
Example 2B Reading a Stem-and-Leaf Plot
Football State
Championship Scores
Team A
Team B
3 7
9522 4 889
865 5 278
51 6 013
2 7
A. Which team had the higher median score?
B. Which team had a wider range of scores?
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Check It Out! Example 2
The temperature in degrees Celsius for two
weeks are given in the stem-and-leaf plot
below. Use the data to answer the following
questions.
Temperature in
Degrees Celsius
Stem
0
1
2
3
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Leaves
7
9
23679
0112456
10-2 Frequency and Histograms
Check It Out! Example 2
Temperature in
Degrees Celsius
Stem Leaves
0 7
1 9
2 23679
3 0112456
A. What was the range of temperatures during
the two weeks?
B. What was the mean temperature during the
two weeks?
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Check It Out! Example 2
Temperature in
Degrees Celsius
Stem Leaves
0 7
1 9
2 23679
3 0112456
C. How many days had temperatures above
freezing?
D. What percent of the days had temperatures
in the 20’s?
Holt McDougal 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. If the data is
divided into intervals, the table shows the
frequency of each interval.
Holt McDougal Algebra 1
10-2 Frequency and Histograms
A histogram is a bar graph used to display
the frequency of data divided into equal
intervals. The bars must be of equal width
and should touch, but not overlap.
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Example 3: Reading a Frequency Table
The numbers of students enrolled in Western
Civilization classes at a university are given on
the frequency table below. Use the table to
answer the following questions.
Enrollment in Western
Civilization Classes
Number
Frequency
Enrolled
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1 – 10
1
11 – 20
21 – 30
4
5
31 – 40
2
10-2 Frequency and Histograms
Example 3: Reading a Frequency Table
Enrollment in Western
Civilization Classes
Number
Frequency
Enrolled
1 – 10
11 – 20
1
4
21 – 30
5
31 – 40
2
A. How many classes have more than 20
students?
B. If a class were selected at random, what is
the probability that the class would have more
than 30 students?
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Check It Out! Example 3
The number of days of Maria’s last 15
vacations are shown on the frequency table
below. Use the table to answer the
following questions.
Number of Vacation Days
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Interval
Frequency
4–6
7–9
5
4
10 – 12
4
13 – 15
2
10-2 Frequency and Histograms
Check It Out! Example 3
Number of Vacation Days
Interval
Frequency
4–6
5
7–9
4
10 – 12
4
13 – 15
2
A. How many more vacations lasted 4 to 6
days than lasted 13 to 15 days?
B. What percent of the vacations lasted 7
to 9 days?
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Example 4
The histogram shows the frequencies for
various enrollments in Civilizations classes.
Use the histogram to answer the following
questions.
A. How many classes
have between 11 and 30
students?
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Example 4
The histogram shows the frequencies for
various enrollments in Civilizations classes.
Use the histogram to answer the following
questions.
B. If you were enrolled
into a class at random,
what is the probability of
there being at most 10
students?
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10-2 Frequency and Histograms
Check It Out! Example 4
The histogram shows the frequency for the
different heights of Black Cherry Trees in an
orchard. Use the histogram to answer the
following questions.
A. For which range of heights
are there the fewest in the
orchard?
B. If a tree were selected at
random, you would expect its
height to be in what range?
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Cumulative frequency shows the frequency of
all data values less than or equal to a given
value. You could just count the number of
values, but if the data set has many values, you
might lose track. Recording the data in a
cumulative frequency table can help you keep
track of the data values as you count.
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Example 4: Making a Cumulative Frequency Table
The weights (in ounces) of packages of
cheddar cheese are given on the table below.
Use the table to answer the following
questions.
Cheddar Cheese
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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: Reading a Cumulative Frequency Table
Cheddar Cheese
Weight
(oz)
Frequency
Cumulative
Frequency
18-20
6
6
21-23
2
8
24-26
5
13
27-29
3
16
A. How many packages weighed less than 24
ounces?
B. What percent of packages weighed less
than 27 ounces?
Holt McDougal Algebra 1
10-2 Frequency and Histograms
Check It Out! Example 5
The number of vowels in each sentence of a
short essay are shown on the cumulative
frequency table below. Fill in the missing
values.
Vowels in Sentences
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Number
Frequency
Cumulative
Frequency
28-31
2
2
32-35
___
9
36-39
5
___
40-43
3
___