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Math 6 NOTES Name ______________________________________
Types of Graphs: Different Ways to Represent Data
Line Graphs
- Line graphs are used to display continuous data.
- Line graphs can be useful in predicting future
events when they show trends over time.
Bar Graphs
- Bar graphs are used to display
categories of data.
- A bar graph is one method of
comparing data by using solid
bars to represent unique
quantities.
Histograms
- A special kind of bar graph that uses bars to
represent the frequency of numerical data
that have been organized into intervals.
- Because the intervals are all equal, all of the
bars have the same width
- Because the intervals are continuous
(connected; ongoing), there is no space between the bars.
Frequency Table
- Frequency tables show the
number of pieces of data that fall
within given intervals.
Line Plot
- Line plots are diagrams that show the frequency of data on a
number line. An “x” is placed above a number on a number line
each time that data value occurs.
Stem and Leaf Plot
Lesson 2–
ATHLETIC SHOES The table shows prices of 20 types of athletic shoes at a recent sidewalk sale. Make a frequency table and then determine how many types are available for less than $80.
Step 1 Choose an appropriate interval and scale for the data. The scale should include the least price, $43, and the greatest price, $135.
Step 2 Draw a table with three columns and label the columns Price , Tally , and Frequency.
Step 3 Complete the table.
Step 4 Two categories include prices less than $80. $40–$59 5 types $60–$79 7 types So, 5 7 or 12 types of shoes cost less than $80.
For Exercises 1 and 2, use the table below.
1. Make a frequency table of the data. 2. Use your frequency table to determine how many students studied 10 hours or more.
A frequency table uses tally marks to show how many times each piece of data appears. If the data is numerical, the table should have a scale which includes the least and the greatest numbers. Also, each table should have an interval which separates the scale into equal parts.
Study Guide and Intervention
Frequency Tables
Price($) Tally Frequency 40–59 5 5 60–79 52 7 80–99 3 3 100–119 2 2 120–139 3 3
Hours Tally Frequency 5 52 51 2
Prices of Athletic Shoes ($) 60 70 43 100
Hours Spent Studying for Math Exam 3 7 10 0 2 12 18 3 1 15 10 11 8 5 9 8 12 6 8 12
Lesson 2–
5. Make a frequency table of the data.
FAVORITE COLORS For Questions 1–3, use the table below. It shows the favorite colors of the students in Mr. Swatzky’s class.
B blue, R red, G green, Y yellow, O orange, P purple
1. Make a frequency table of the data. Favorite Color
Practice: Word Problems
Frequency Tables
Tally Frequency
Holidays Tally Frequency
HOLIDAYS For Questions 4–6, use the table below. It shows the number of holidays in each month of 2003.
2. If one student changed his or her vote from blue to yellow, what would be the favorite color of most students? 3. If one student changed his or her vote from red to purple, what would be the favorite color of the fewest students? 4. What is wrong with using the intervals 1–2, 3–4, and 5–6 to represent the data in a frequency table? 6. What is the interval and scale of your frequency table from Question 5?
Favorite Colors of Mr. Swatzky’s Students B R R O B Y G G P B Y B B Y R O B R B Y G B O Y B Y G G G G P Y R R G
2003 Holidays 3 5 5 5 4 4 1 0 2 6 5 2
Lesson 2–
SHOE SIZE The table shows the shoe size of students in Mr. Kowa’s classroom. Make a line plot of the data.
Step 1 Draw a number line. Because the smallest size is 4 and the largest size is 14, you can use a scale of 4 to 14 and an interval of 2.
Step 2 Put an “” above the number that represents the shoe size of each student.
Use the line plot in Example 1. Identify any clusters, gaps, or outliers and analyze the data by using these values. What is the range of data?
Many of the data cluster around 6 and 10. You could say that most of the shoe sizes are 6 or
- There is a gap between 11 and 14, so there are no shoe sizes in this range. The number 14 appears removed from the rest of the data, so it would be considered an outlier. This means that the shoe size of 14 is very large and is not representative of the whole data set.
The greatest shoe size is 14, and the smallest is 4. The range is 14 – 4 or 10.
PETS For Exercises 1–3 use the table at the right that shows the number of pets owned by different families.
1. Make a line plot of the data. 2. Identify any clusters, gaps, or outliers. 3. What is the range of the data?
Study Guide and Intervention
Line Plots
A line plot is a diagram that shows the frequency of data on a number line.
Shoe Sizes 10 6 4 6 5 11 10 10 6 9 6 8 7 11 7 14 5 10 6 10
Number of Pets 2 1 2 0 3 1 1 2 8 3 1 4
4 6 8 10 12
14
TELEVISION SETS For Exercises 1–6, use the table below. It shows the number of television sets owned by 30 different families.
Lesson 2–
Practice: Word Problems
Line Plots
1. Make a line plot for the data. 2. How many televisions do most families own? 3. What is the greatest number of televisions owned by a family? 4. What is the range of the data? 5 5. Identify any clusters, gaps, or outliers, if any exist, and explain what they mean. 6. Describe how the range of the data would change if 5 were not part of the data set.
Number of TVs 2 1 2 4 3 0 2 3 2 3 4 2 1 2 2 3 4 0 3 1 3 2 1 2 5 3 4 3 0 0
Lesson 2–
ENDANGERED SPECIES For Exercises 1–6, use the table below. It shows the number of endangered species in the U.S.
Practice: Word Problems
Stem-and-Leaf Plots
1. Make a stem-and-leaf plot of the data. 2. What group has the greatest number of endangered species in the U.S.? 3. What group has the least number of endangered species in the U.S.? 4. What is the range of the data? 68 5. Use your stem-and-leaf plot to determine the median and mode. 6. How many groups have less than 30 endangered species in the U.S.?
Group
Number of Species
Group
Number of Species mammals 63 clams 61 birds 78 snails 20 reptiles 14 insects 33 amphibians 10 arachnids 12 fishes 70 crustaceans 18
Endangered Species in U.S.
Make a bar graph of the data. Compare the number of students in jazz class with the number in ballet class.
Step 1 Decide on the scale and interval.
Step 2 Label the horizontal and vertical axes.
Step 3 Draw bars for each style.
Step 4 Label the graph with a title.
About twice as many students take ballet as take jazz.
Make a line graph of the data. Then describe the change in Gwen’s allowance from 1998 to 2002.
Step 1 Decide on the scale and interval.
Step 2 Label the horizontal and vertical axes.
Step 3 Draw and connect the points for each year.
Step 4 Label the graph with a title.
Gwen’s allowance did not change from 1998 to 1999 and then increased from 1999 to 2002.
Make the graph listed for each set of data.
1. bar graph 2. line graph
199719981999200020012002
10
12
14
16
18
20
22
24
26
Amount ($)
Year
0
Gwen's Allowance
Ballet Tap Jazz
6
8
4
0
2
10
12
Students
Style
Modern
Dance Class Attendance
A graph is a visual way to display data. A bar graph is used to compare data. A line graph is used to show how data changes over a period of time.
Study Guide and Intervention
Bar Graphs and Line Graphs
Dance Classes Style Students
Ballet Tap Jazz Modern
Gwen’s Allowance Year 1997 1998 1999 2000 2001 2002 Amount ($) 10 15 15 18 20 25
Getting Ready for School Day Time (min) Monday Tuesday Wednesday Thursday Friday
Riding the Bus Student Time (min) Paulina Omar Ulari Jacob Amita
Lesson 2–
SIBLINGS Make a bar graph to display the data in the table below.
Step 1 Draw a horizontal and a vertical axis. Label the axes as shown. Add a title.
Step 2 Draw a bar to represent each student. In this case, a bar is used to represent the number of siblings for each student.
SIBLINGS The number of siblings of 17 students have been organized into a table. Make a histogram of the data.
Step 1 Draw and label horizontal and vertical axes. Add a title.
Step 2 Draw a bar to represent the frequency of each interval.
1. Make a bar graph for the data in 2. Make a histogram for the data in the table. the table.
0–1 2–3 4–5 6–
8
10
4
6
0
Frequency^2
Number of Siblings
Siblings
Sue Istu Margarita
3
4 2 0
1
5
6
7
Number of Siblings
Student
Akira
Siblings
Study Guide and Intervention
Bar Graphs and Histograms
A bar graph is one method of comparing data by using solid bars to represent quantities. A histogram is a special kind of bar graph. It uses bars to represent the frequency of numerical data that have been organized into intervals.
Student
Number of Siblings Sue Isfu Margarita Akira
Student
Number of Free Throws Luis Laura Opal Gad
Number of Free Throws Frequency 0–1 1
Number of Siblings
Frequency
0–1 4
PUPPIES For Exercises 1 and 2, use the EARTH SCIENCE In Exercises 3–6, use table below. It shows the results of a the table below. It shows the highest survey in which students were asked wind speeds in 30 U.S. cities. what name they would most like to give a new pet puppy.
Lesson X–
Lesson 2–
Practice: Word Problems
Bar Graphs and Histograms
Highest Wind Speeds (mph) 52 75 60 80 55 54 91 60 81 58 53 73 46 76 53 46 73 46 51 49 57 58 56 47 65 49 56 51 54 51
Name Votes Max 15 Tiger 5 Lady 13 Shadow 10 Molly 9 Buster 2
1. Make a bar graph to display the data.
Favorite New Puppy Names
2. Use your bar graph from Exercise 1. Compare the number of votes the name Shadow received to the number of votes the name Tiger received. 3. Make a histogram of the data. Highest Wind Speeds 4. What is the top wind speed of most of the cities? 5. How many cities recorded wind speeds of 80 miles per hour or more? 6. How many cities recorded their highest wind speeds at 60 miles per hour or more?
1. INCOME The bar graphs below show the total U.S. national income (nonfarm). Which graph could be misleading? Explain.
GEOGRAPHY For Exercises 2–4, use the table that shows the miles of shoreline for five states.
2. Find the mean, median, and mode of the data. 3. Which measure of central tendency is misleading in describing the miles of shoreline for the states? Explain. 4. Which measure of central tendency most accurately describes the data?
'60 '70 '80 '
20
30
15
0
10
40
300
700
Income in Billions of
Current Dollars
Year
'
Graph B U.S. Nonfarm Income
'60 '70 '80 '
200
300
100 0
400
500
600
700
Income in Billions of
Current Dollars
Year
'
Graph A U.S. Nonfarm Income
Lesson X–
Practice: Skills
Misleading Statistics
Lesson 2–
Miles of Shoreline
State
Virginia 3,
Maryland 3,
Washington 3,
North Carolina 3,
Pennsylvania 89
Length of Shoreline (mi)
