Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
(For help, go to Lesson 3-3.)
Find the median and mode of each data set.
1. 6, 9, 9, 5, 9
2. 73, 78, 77, 73, 79
3. 300, 100, 200, 150, 300
4. 3, 5, 7, 9, 3, 4, 6, 3, 7
Check Skills You’ll Need
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
Solutions
1. 5, 6, 9, 9, 9
median = 9
mode = 9
2. 73, 73, 77, 78, 79
median = 77
mode = 73
3. 100, 150, 200, 300, 300
median = 200
mode = 300
4. 3, 3, 3, 4, 5, 6, 7, 7, 9
median = 5
mode = 3
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
Quick Check
A survey asked 22 students how many hours of TV
they watched daily. The results are shown. Display the data
in a frequency table.
1 3 4 3 1 1 2 3 4 1 3
2 2 1 3 2 1 2 3 2 4 3
List the numbers of
hours in order.
Use a tally mark
for each result.
Count the tally marks and
record the frequency.
Number
Tally
Frequency
1
|||| |
6
2
|||| |
6
3
|||| ||
7
4
|||
3
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
Twenty-one judges were asked how many cases they were trying
on Monday. The frequency table below shows their responses. Display the
data in a line plot. Then find the range.
“How many cases are you trying?”
Number Frequency
0
3
1
5
2
4
3
5
4
4
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
(continued)
For a line plot, follow these steps 1 , 2 , and 3 .
3 Write a title that describes the data.
Cases Tried by Judges
x
x
x
x
x
x
x
x
0
1
x
x
x
x
x
x
x
x
x
x
x
x
x
2
3
4
2 Mark an x for each
response.
1 Draw a number line with the choices below it.
The greatest value in the data set is 4 and the least value is 0. So the
range is 4 – 0, or 4.
Quick Check
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
Solve.
1. Maria surveyed friends to find out how
many pets each one has.
The responses are below.
Display the data in a frequency table.
0, 1, 1, 2, 3, 0, 1, 1, 3, 2, 1, 2, 1, 0, 1, 0, 0
Pets
0
1
2
3
2. Here are the numbers of books students
read in the last month: 5, 4, 0, 12, 4, 5,
4, 3, 10, 5, 12, 3, 5, 7, 3, 10, 5, 0, 6.
Display the data in a line plot.
Then find the range.
range: 12
12-1
Tally Frequency
IIII
5
IIII II
7
III
3
II
2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
(For help, go to Lesson 3-3.)
Find each median.
1. 12, 10, 11, 7, 9, 8, 10, 5
2. 4.5, 3.2, 6.3, 5.2, 5, 4.8, 6, 3.9
3. 55, 53, 67, 52, 50, 49, 51, 52, 52, 52
4. 101, 100, 100, 105, 102, 101
Check Skills You’ll Need
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
Solutions
1. 5, 7, 8, 9, 10, 10, 11, 12
median =
9 + 10
= 9.5
2
2. 3.2, 3.9, 4.5, 4.8, 5, 5.2, 6, 6.3
median =
4.8 + 5
= 4.9
2
3. 49, 50, 51, 52, 52, 52, 52, 53, 55, 67
median =
52 + 52
= 52
2
4. 100, 100, 101, 101, 102, 105
median =
101 + 101
= 101
2
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
The data below represent the wingspans in
centimeters of captured birds. Make a box-and-whisker plot.
61 35 61 22 33 29 40 62 21 49 72 75 28 21 54
Step 1 Arrange the data in order from least to greatest. Find the median.
21 21 22 28 29 33 35 40 49 54 61 61 62 72 75
Step 2 Find the lower quartile and upper quartile, which are the medians of the
lower and upper halves.
21 21 22 28 29 33 35 40 49 54 61 61 62 72 75
lower quartile = 28
upper quartile = 61
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
(continued)
Step 3 Draw a number line.
Mark the least and greatest values, the median, and the quartiles.
Draw a box from the first to the third quartiles.
Mark the median with a vertical segment.
Draw whiskers from the box to the least and greatest values.
Quick Check
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
Use box-and-whisker plots to compare test scores from
two math classes.
Class A: 92, 84, 76, 68, 90, 67, 82, 71, 79, 85, 79
Class B: 78, 93, 81, 98, 69, 95, 74, 87, 81, 75, 83
Draw a number line for both sets of data. Use the range of data
points to choose a scale.
Draw the second box-and-whisker plot below the first one.
Quick Check
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
Describe the data in the box-and-whisker plot.
The lowest score is 55 and the highest is 85.
One fourth of the scores are at or below 66 and one fourth of the scores
are at or above 80.
Half of the scores are at or between 66 and 80 and thus within 10 points
of the median, 76.
Quick Check
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
The plots below compare the percents of students who
were eligible to those who participated in extracurricular activities
in one school from 1992 to 2002. What conclusions can you draw?
About 95% of the students were eligible to participate in extracurricular
activities.
Around 60% of the students did participate.
A little less than two thirds of the eligible students participated in
Quick Check
extracurricular activities.
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
Solve.
1. Use the data to make a box-and-whisker plot.
Student heights (in.) are: 60, 66, 59, 67, 68, 63, 62, 61, 69, 64, 61.
a. What is the median height?
63 in.
b. Between what heights do 50% of the students fall?
between 61 in. and 67 in.
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
2. The box-and-whisker plots below compare prices for the same items
at Mary’s Discount Store and Ed’s Clothing. What conclusions can
you draw?
Prices at the discount store are more tightly grouped around the median
price of $25. Half the items cost from $18 to $45. For less expensive
items, there is not much difference in the prices at the two stores. For
more expensive items, the discount store offers lower prices.
12-2