1. Chapter 4: Probability & Statistics
Section 4.5: Charts & Graphs
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

2. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Organizing Data
We will examine how to read and create several types of charts and graphs.
Stem-and-Leaf Plots: Displays Groups of Numerical Data
Bar Graphs: Graphical Representation of Data into Disjointed Bins
Histograms: Graphical Representation of Data into Continuous Bins
Line Graphs: Graphical Representation of Data Showing Change over Time
Pie Charts: Used to Show Relative Proportions of Data in Relation to the Entire Data Set
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Stem-and-Leaf Plots
For two-digit numbers, group the data into similar ranges according to the tens digits. That is, group together all the numbers in the 90s, the 80s, 70s, and so on.
When putting them into a stem-and-leaf chart, the tens digits are the “stems,” and the ones digit for each number is a “leaf.”
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

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Stem-and-Leaf Plots
Example: Create a stem-and-leaf chart for the following data. 56, 90, 94, 88, 57, 78, 87, 87, 89, 87, 65, 59, 88, 99
STEM
LEAVES 9 8 7 6 5
STEM
LEAVES 9 8 7 6 5
STEM
LEAVES
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

5. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Stem-and-Leaf Plots
Example: Create a stem-and-leaf chart for the following data. 56, 90, 94, 88, 57, 78, 87, 87, 89, 87, 65, 59, 88, 99
STEM
LEAVES 9 8 7 6 5
STEM
LEAVES 9 8 7 6 5
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

6. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Stem-and-Leaf Plots
Example: Create a stem-and-leaf chart for the following data. 56, 90, 94, 88, 57, 78, 87, 87, 89, 87, 65, 59, 88, 99
STEM
LEAVES 9 8 7 6 5
STEM
LEAVES 9
0 4 8 7 6 5
STEM
LEAVES 9 8 7 6 5
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

7. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Stem-and-Leaf Plots
Example: Create a stem-and-leaf chart for the following data. 56, 90, 94, 88, 57, 78, 87, 87, 89, 87, 65, 59, 88, 99
STEM
LEAVES 9 8 7 6 5
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

8. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Stem-and-Leaf Plots
Example: Create a stem-and-leaf chart for the following data. 56, 90, 94, 88, 57, 78, 87, 87, 89, 87, 65, 59, 88, 99
STEM
LEAVES 9 8 7 6 5
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

9. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Bar Graphs
Group the data into categories (called bins) - in any order - and list the name of each bin under the horizontal axis.
Label the vertical axis with numbers, starting at 0, and equally spacing the intervals, going as high as needed.
Create a bar for each distinct bin, with the height of the bar indicating the number of items in the corresponding bin.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

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Bar Graphs
Example: A bag contains 6 red jellybeans (R), 2 green jellybeans (G), 7 yellow jellybeans (Y), and 4 blue jellybeans (B). Create a bar graph that displays this data. 6- 4- 2-
R G Y B
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Histograms
A histogram is very similar to a bar chart.
In a bar chart the bins are separate and distinct, and can be put in any order.
In a histogram, the bars represent continuous bins (usually time periods), and must be in order, with no gaps between them.
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

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Histograms
Example: The table below represents the number of students taking MATH 104B in five consecutive fall and spring semesters. Create a histogram for the data.
Semester
Students
Fall ‘12
450
Spring ‘13
505
Fall ‘13
420
Spring ‘14
598
Fall ‘14
618
700 -
600 -
500 -
400 -
300 -
200 -
100 -
| | | | |
F12 S13 F13 S14 F14
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Line Graphs
Line graphs are used to emphasize the change in data over time. Where the focus on a histogram is the height of the individual bars, the focus on a line graph is the slope of the lines between each bin.
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Pie Charts
Pie charts are a way to represent 100% of a data set, where each disjoint (non-overlapping) group in the set is represented by an appropriately sized sector.
The size of the sector is determined by the percent of the group size in the data set.
Once we have the percent of the data, we multiply that percent by 360o to get the number of degrees of the sector.
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Pie Charts
Example: In a recent student council election, 40 students voted for Al, 20 voted for Beth, 50 voted for Cindy, and 90 voted for Dave. Create a pie chart that represents these results.
There were = 200 voters.
Al got 40/200 = 0.2 = 20% of the votes.
20% of 360o = 0.2(360o) = 72o
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16. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Pie Charts
Example: In a recent student council election, 40 students voted for Al, 20 voted for Beth, 50 voted for Cindy, and 90 voted for Dave. Create a pie chart that represents these results.
There were = 200 voters.
Al got 40/200 = 0.2 = 20% of the votes.
20% of 360o = 0.2(360o) = 72o
Beth got 20/200 = 0.1 = 10% of the votes.
10% of 360o = 0.1(360o) = 36o
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

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Pie Charts
Example: In a recent student council election, 40 students voted for Al, 20 voted for Beth, 50 voted for Cindy, and 90 voted for Dave. Create a pie chart that represents these results.
There were = 200 voters.
Al got 40/200 = 0.2 = 20% of the votes.
20% of 360o = 0.2(360o) = 72o
Beth got 20/200 = 0.1 = 10% of the votes.
10% of 360o = 0.1(360o) = 36o
Cindy got 50/200 = 25% of the votes.
25% of 360o = 0.25(360o) = 90o
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

18. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Pie Charts
Example: In a recent student council election, 40 students voted for Al, 20 voted for Beth, 50 voted for Cindy, and 90 voted for Dave. Create a pie chart that represents these results.
There were = 200 voters.
Al got 40/200 = 0.2 = 20% of the votes.
20% of 360o = 0.2(360o) = 72o
Beth got 20/200 = 0.1 = 10% of the votes.
10% of 360o = 0.1(360o) = 36o
Cindy got 50/200 = 25% of the votes.
25% of 360o = 0.25(360o) = 90o
Dave got 90/200 = 45% of the votes.
45% of 360o = 0.45(360o) = 162o
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

19. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Pie Charts
Example: In a recent student council election, 40 students voted for Al, 20 voted for Beth, 50 voted for Cindy, and 90 voted for Dave. Create a pie chart that represents these results.
There were = 200 voters.
Al got 40/200 = 0.2 = 20% of the votes.
20% of 360o = 0.2(360o) = 72o
Beth got 20/200 = 0.1 = 10% of the votes.
10% of 360o = 0.1(360o) = 36o
Cindy got 50/200 = 25% of the votes.
25% of 360o = 0.25(360o) = 90o
Dave got 90/200 = 45% of the votes.
45% of 360o = 0.45(360o) = 162o
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates