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MATH009 Probability and Statistics Handout # 5

Graphical Presentation of Data

Raw data by themselves do not convey much information. Thus, the data must be turned into something

informative by using tables, graphs, or charts.

When constructing your graphs, make sure that they contain a clear title. The axes should be labeled,

and the scales should begin with a zero point. If lack of space makes it inconvenient to use a zero point,

a scale break may be inserted to indicate its omission. Also, indicate the sample size. Simplicity and

honesty must be observed. Do not distort the graph by exaggerating or omitting details.

Graphs for Qualitative Data

We can summarize categorical or qualitative data using a bar graph or a pie chart.

In a bar graph, the categories are written in the horizontal axis (which can be in any order) while the

frequencies or relative frequencies are written in the vertical axis. The spaces between the bars are

equal, and the height of each bar is proportional to the frequency or relative frequency in each category.

Example Favorite Colors of the Class

Frequency

Yellow Red Blue Green Pink

In a pie chart, the slices must be proportional to the frequency or relative frequency in each category. To

get the angle measure for a slice, multiply the relative frequency of that category by 360 degrees.

Example: Favorite Types of Movie

Action, Comedy, Drama,

Horror, Romance, Sci-Fi

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Graphs for Quantitative Data

We can summarize numerical or quantitative data using a histogram, a line graph, or a stem-and-leaf plot.

In a histogram, the horizontal axis represents the quantitative variable, whereas the vertical axis represents the frequency or relative frequency. Note that a histogram differs in a bar chart in the types of data it can handle. Usually, there are no spaces between classes in histograms as there are in bar charts for category data.

Example: Refer to the car mileage example from handout 3.

Frequency Distribution Table of Car Mileage

Class Interval Tally Frequency Relative Frequency

100 − 109 | | | | 4 110 − 119 0

10% 0%

120 − 129 | | | 3 7.5% 130 − 139 | | | | | | 7 17.5% 140 − 149 | | | | | | | | | 11 27.5% 150 − 159 | | | | | | | 8 20% 160 − 169 | | | | 5 12.5% 170 − 179 0 180 − 189 | | 2

0% 5%

n = 40 100%

Histogram of Car Mileage Frequency

12

10

8

6

4

2

0 100 110 120 130 140 150 160 170 180 190 Mileages

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A stem and leaf plot displays the data by sorting them into stems and leaves. It is shaped like the histogram, though shown horizontally. However, unlike the histogram, it retains all the original information as the numbers themselves are included in the plot. When setting up a stem and leaf plot, it is important to provide a legend. Example:

Stem and Leaf Plot of Car Mileage Frequency Stem Leaf

4 10 | 5789 0 11 | 3 12 | 568 7 13 | 2555688 11 14 | 00244556689 8 15 | 00234678 5 16 | 13458 0 17 | 2 18 | 36 _________

n = 40 Legend: 12 | 3 = 123

Exercises:

1. What is/are the difference(s) between a histogram and a bar graph?

2. What is/are the difference(s) between a histogram and a stem-and-leaf display?

3. How do we decide which graph to use (bar graph, pie chart, histogram, and stem-and-leaf)?

4. A traffic inspector has counted the number of automobiles passing a certain point in 100 successive 20-minute time periods. The observations are listed below.

23 20 16 18 30 22 26 15 5 18

14 17 11 37 21 6 10 20 22 25

19 19 19 20 12 23 24 17 18 16

27 16 28 26 15 29 19 35 20 17

12 30 21 22 20 15 18 16 23 24

15 24 28 19 24 22 17 19 8 18

17 18 23 21 25 19 20 22 21 21

16 20 19 11 23 17 23 13 17 26

26 14 15 16 27 18 21 24 33 20

21 27 18 22 17 20 14 21 22 19

Construct a frequency distribution table and a histogram for this data set. Use the lowest value as the starting point and a class width of 5.

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A line graph is used to describe a trend pictorially. It shows time on the horizontal axis and the

frequencies (or percentages or rates) of another variable on the vertical axis.

Example:

Questions:

1. What is the line graph about?

2. What is the busiest time of day at the store?

3. At what time does business start to slow down?

4. How many people are in the store when it opens?

5. About how many people are in the store at 2:30 pm?

6. What was the greatest number of people in the store?

7. What was the least number of people in the store?