Name______________________________
Name______________________________ Date_______________
Integrated Algebra A
Notes/Homework Packet 4
|Lesson |Homework |
|Bar Graphs |HW #1 |
|Frequency Table & Histograms |HW #2 |
|Mean, Median, Mode, & Range |HW #3 |
|Stem-and-Leaf Plot |HW #4 |
|Box-and-Whisker Plot |HW #5 |
|Line Graphs & Interpreting Circle Graphs |HW #6 |
|Review Activity | |
|Review Sheet | |
|Test 4 | |
Bar Graphs
There are several ways to organize and display data. Here a some:
Tables, bar graphs, frequency histograms, line graphs, and circle graphs.
Today, we will learn about Bar Graphs. Let’s start with an example:
Example 1: Organize the data into a frequency table and make a bar
graph. The following are the ages when a randomly chosen
group of 20 teenagers received their driver’s licenses:
18 17 16 16 17 16 16 16 19 16 16 17 16 17 18 16 18 16 19 16
|Age License Received | | | | |
|Frequency | | | | |
STEPS:
1) First, choose a scale. Since for this example, the data range from 2 to 11,
make the scale increase from 0 to 12 by ones.
2) Draw and label the axes. Mark intervals on the vertical axis according to the
scale you chose.
3) Draw a bar for each category.
4) Give the bar graph a title.
Bar graphs do not always deal with frequencies. See Example 2 on back!
Example 2: The table shows the number of gallons of water needed to
produce one pound of some foods. Make a bar graph of
the data.
|Food (1 lb) |lettuce |tomatoes |carrots |broccoli |corn |
|Water (gallons) |21 |29 |40 |42 |119 |
Follow the steps from the 1st page!
ACTIVITY: Two boys and two girls will be randomly selected. Their heights will be
measured, entered in the table, and (bar) graphed on the grid.
|Name | | | | |
|Height (in) | | | | |
Name_____________________________ Date_______________
HW #1
|Field Location |Number of Home Runs |
|left |31 |
|left-center |21 |
|center |15 |
|right-center |3 |
|right |0 |
1. In 1998, baseball player Mark McGwire hit a
record 70 home runs. The table shows the
locations to which the home runs were hit.
Draw a bar graph to display the data.
2. The bar graph shows the total amount of dairy products, vegetables, and fruit
consumed by Americans in a given year.
a. Compare 1995 to 1970. What is the difference?
b. Explain why the graph could be misleading.
Frequency Table & Histograms
A histogram is a type of bar graph, which shows the frequency of something happening.
To construct a frequency table:
▪ Use three columns: Intervals, Tally, and Frequency.
▪ The intervals must be of equal length.
▪ Use tally marks to count the data.
▪ After data is tallied, record the count for each interval in the frequency column.
Example 1
Christine took a survey of 15 people to find out how many pages were in the last book they read. Her data consisted of the following numbers:
397, 90, 165, 100, 205, 270, 85, 150, 310, 450, 45, 190, 250, 101, and 97
a) Construct a frequency table for the given data.
|Interval |Tally |Frequency |
|(pages) | | |
|0-99 | | |
|100-199 | | |
|200-299 | | |
|300-399 | | |
| 400-499 | | |
b) Construct a frequency histogram using the table completed in part a.
Example 2
Josh’s math grades for one marking period were 85, 72, 97, 81, 77, 93, 100, 75, 86, 70, 96, and 80.
a) Construct a frequency table for the given data.
|Interval |Tally |Frequency |
|(grades) | | |
| 61-70 | | |
|71-80 | | |
|81-90 | | |
| 91-100 | | |
b) Construct a frequency histogram using the table completed in part a.
Example 3: This chart shows the number of times a person blinked in one minute. Construct a frequency histogram given the table.
|Interval |Frequency |
|(# of blinks) | |
| 0-10 | 45 |
|11-20 |50 |
|21-30 |65 |
| 31-40 |20 |
Name______________________________ Date______________________
HW #2
1. (a) Construct a frequency table for the weight, in pounds, of 20 students in an
elementary school class:
72, 64, 56, 60, 66, 72, 48, 66, 58, 60, 60, 50, 68, 72, 68, 62, 72, 58, 60, and 68.
|Interval |Tally |Frequency |
|(weights) | | |
|45-49 | | |
| 50-54 | | |
|55-59 | | |
|60-64 | | |
|65-69 | | |
| 70-74 | | |
(b) Construct a frequency histogram using the table from part a.
1. What are some differences you see between a bar graph and a histogram?
2. Do you remember how to find average? Find the average of the following numbers: 65, 80, 96, 50, and 73.
Mean, Median, Mode, & Range
Vocabulary:
Mean: ____________________________________________________________________________
__________________________________________________________________________________
Median: _________________________________________________________________________
__________________________________________________________________________________
Mode: ___________________________________________________________________________
__________________________________________________________________________________
Range: __________________________________________________________________________
__________________________________________________________________________________
Example 1
Find the mean, median, mode, and range of the data set.
4, 8, 8, 3, 6, 8, 3
mean:
median:
mode:
range:
Example 2
Find the mean, median, mode, and range of the data set.
9, 6, 91, 5, 7, 6, 8, 8, 7, 9
mean:
median:
mode:
range:
Example 3
Find the mean, median, mode, and range of the data set.
28, 12, 101, 53
mean:
median:
mode:
range:
Practice:
|Planet |Known |
| |Moons |
|Mercury |0 |
|Venus |0 |
|Earth |1 |
|Mars |2 |
|Jupiter |39 |
|Saturn |30 |
|Uranus |21 |
|Neptune |8 |
|Pluto |1 |
1) Use the data in the table to find each answer.
(Round to the nearest tenth if necessary)
a) Find the average number of moons for the
terrestrial planets: Mercury, Venus, Earth, and Mars.
b) Find the average number of moons for the gas
giants: Jupiter, Saturn, Uranus, and Neptune.
c) Find the average number of moons for all the planets.
Review:
1. Simplify: a. 3(p + 7) – 5p b. 8 + 7(y + 5) – 3
2. Solve: a. 16 – 8r = 40 b. 4x – 3(x – 2) = 21
Name_____________________________ Date_______________
HW #3
Round to the nearest tenth if necessary to round.
For #1 and 2, find the mean, median, mode, and range of the following data sets:
1) 4, 2, 10, 6, 10, 7, 10
2) 3.56, 4.40, 6.25, 1.20, 8.52, 1.20
3) The table shows the number of shutouts that ten baseball pitchers had in their
careers. A shutout is a complete game pitched without allowing a run.
|Pitcher |Shutouts |
|Warren Spahn |63 |
|Christy Mathewson |80 |
|Eddie Plank |69 |
|Nolan Ryan |61 |
|Bert Blyleven |60 |
|Walter Johnson |110 |
|Cy Young |76 |
|Tom Seaver |61 |
Find the mean, median, mode, and range
for the set of data.
Stem-and-Leaf Plot
Another way to display data is by using a stem-and-leaf plot.
Example 1
Arrange the given data values into a stem-and-leaf plot.
2, 5, 13, 13, 17, 18, 20, 22, 26, 31, and 37.
The data range from 2 to 37, so stems are 0 to 3.
Example 2
Use the given data to make a stem-and-leaf plot.
|Atomic Numbers of Some Elements |
|Hydrogen 1 |Silver 47 |Carbon 6 |Titanium 22 |
|Nitrogen 7 |Barium 56 |Argon 18 |Bromine 35 |
|Calcium 20 |Iron 26 |Krypton 36 |Iodine 53 |
Example 3
Use the given data to make a stem-and-leaf plot.
142, 137, 150, 148, 142, 130, 168, 122, 165, 160, 145, 151, 104, 113
Example 4
List the data values in the stem-and-leaf plot given below and find the median.
Name_____________________________ Date_______________
HW #4
1.
2. List the data values in the stem-and-leaf plot given below and find the mode.
Review:
1. Three times the sum of a number and 2 exceeds the number by 14. Translate
the sentence and Find the number (SOLVE)!
Box-and-Whisker Plots
Another way we can organize data is by putting the values into a box and whisker plot.
We know that the median of a set of data separates the data into two equal parts.
Data can be further separated into quartiles (four equal parts).
The first quartile is the median of the lower part of the data.
The second quartile is another name for the median of the entire set of data.
The third quartile is the median of the upper part of the data.
Constructing a Box-and-Whisker Plot
Example 1
The data: Math test scores 80, 75, 90, 95, 65, 65, 80, 85, 70, 100, 80
Step 1: Write the numbers in order.
Step 2: Find the following:
a) Smallest Value:
b) 1st Quartile:
c) Median:
d) 3rd Quartile:
e) Largest Value:
Step 3: Draw a number line.
Step 4: Place a dot below each value listed in step 2.
Step 5: Draw a box with ends through the points for the first and third
quartiles. Then draw a vertical line through the box at the
median point. Now, draw the whiskers (or lines) from each end of
the box to the smallest and largest values.
Draw box-and-whisker plot below for Example 1.
Example 2
Create a box-and-whisker plot using this set of data:
22, 17, 22, 49, 55, 21, 49, 62, 21, 16, 18, 44, 42, 48
Smallest Value:
1st Quartile:
Median:
3rd Quartile:
Largest Value:
Example 3
|3. |
|[pic] |
|According to the box and whisker plot shown at the left, what is: |
|the median? |
|the first quartile? |
|the third quartile? |
|the smallest value? |
|the largest value? |
| |
| |
| |
| |
| |
Plotting Box-and-Whisker Plot on Calculator
• Press
• Select Edit
o Enter values into L1 (Press enter after each value)
• Press
o Choose #1
o Choose ON
o Chose Picture of Box and Whisker
• Press
o Choose #9 (Zoom Stat)
• Use and Arrow Keys to move around
o minX =
o Q1 =
o med =
o Q3 =
o maxX =
This is a great way to check that you have the correct values before you draw a box-and-whisker plot by hand!
Name______________________________ Date________________
HW #5
1. Create a box and whisker plot using the data: 85, 92, 78, 88, 90, 88, 89
Smallest Value:
1st Quartile:
Median:
3rd Quartile:
Largest Value:
2. Create a box and whisker plot using the data:
14, 12, 15, 17, 15, 16, 17, 18, 15, 19, 20, 17
Smallest Value:
1st Quartile:
Median:
3rd Quartile:
Largest Value:
Review:
1. Find the following for question #2 above:
Mean:
Median:
Mode:
Range:
Line Graphs & Interpreting Circle Graphs
A Line Graph is often used to show trends or to make estimates for values between data points. In other words, it can be used to show how data changes over time.
Some Real-Life Uses: To track stock performance, to monitor a patient’s blood pressure, etc.
Example 1: Make a line graph of the given data. Use the graph to estimate the number of tornados that occurred in 1995.
|Number of Tornadoes in Illinois by Year |
|Year |Tornadoes |
|1988 |20 |
|1990 |50 |
|1992 |23 |
|1994 |20 |
|1996 |61 |
|1998 |110 |
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Example 2: Make a line graph of the given data. Use the graph to estimate the life
|Life Expectancy by Birth Year (U.S.) |
|Year |1970 |1975 |1980 |1985 |1990 |
|Age |70.8 |72.6 |73.7 |74.7 |75.4 |
expectancy of someone born in 1982.
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Circle graphs (or pie charts) are another way we can display data about many things. It is important to be able to interpret graphs such as these as well.
Example 1:
1. How many students are there in the class? ____________
2. Which sports do the students favor? ____________
3. Which sport was like by six people? ____________
4. How many more people like swimming than baseball? ____________
5. Which sports were liked by the same amount of students? ____________
Example 2:
Below is a circle graph showing the breakdown of Katie’s 24-hour day. Answer the questions below based on the graph.
1. How many hours a day does Katie spend watching television? ______
2. How many hours a day does she spend on school and homework combined?____
3. What percentage of Katie’s day does she spend sleeping? ______
4. What percentage of Katie’s day is taken up by homework, school, and eating?___
Name _________________________ Date ____________
HW #6
1. A science class recorded the highest temperature each day from December 1 to
December 14. The temperatures are given in the table. Draw a line graph to
|Date |1 |2 |3 |4 |5 |6 |7 |
|Temp. ([pic]) |40 |48 |49 |61 |24 |35 |34 |
display the data.
|Date |8 |9 |10 |11 |12 |13 |14 |
|Temp. ([pic]) |42 |41 |40 |22 |20 |28 |30 |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
2. The circle graph represents marbles in a jar.
a. How many marbles are in the jar? ______
b. Which color marbles show up the most in the jar? ____
c. How many black marbles are in the jar? ______
d. What percentage of marbles in the jar are black? ____
e. What percentage of marbles are purple? ______
3. a. Which day did the
kite reach its highest height? _______________
b. How much higher
did the kite fly on Thursday than Monday?_________
c. How many days did
the kite fly lower than 80 ft?_____________
-----------------------
The number of times each value occurs
x:
y:
We will use a “break” on the vertical axis.
There should be no spaces between the bars!
When our intervals don’t start at zero, we have to draw a “break”.
Place numbers in order first!
Place numbers in order first!
Place numbers in order first!
Put leaves in order!
Stem:
First digit
Leaf: Last digit
KEY:
Stem:
First digits
Leaf: Last digit
0
1
2
3
4
5
1 3 6
5
0 3
1 2
4 5 9
1 1 2 2
Key: 1 5 = 15
0
1
2
3
1 5 7
2 4 6 8
0 1 7 9
3 3 4 6
Key: 2 1 means 21
What if there is no middle???
2nd
Y =
STAT
ENTER
ENTER
ZOOM
ENTER
TRACE
2
8
2
3
8
1
[pic]
[pic]
[pic]
[pic]
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