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Data Display Choices

Associate data displays with appropriate conclusions.

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Data Display Choices

License: CC BY-NC 3.0

Rahul has just moved to California from Arizona. Everyone around him is talking about the California drought, but he is having trouble understanding what they mean since California has so much more rain than he was used to in Arizona. He found a table that compares the rainfall of the past 50 years to the average rainfall over 135 years. He wants to create some sort of visual representation that will clarify the data, but he's not sure which type of graph he should choose.

In this concept, you will learn how to display data in different formats for best effectiveness.

Choices for Data Display

Data is a collection of numbers brought together in order for analysis. Temperature, rainfall, salinity, money spent, percentage of minority students, etc. are all different types of data.

Often, raw data will be displayed in a table which is organized in some sort of clear order but without any analysis having been performed.

A graph is a way of representing data that includes analysis. The right graph for the data set will make important trends in the data clear. There are many different kinds of graphs, and each is particularly effective with different kinds of data.

A bar graph displays the frequency of data, or how often data occurs. Here is an example.

License: CC BY-NC 3.0

double bar graph compares the frequency of two sets of data. Here is an example.

License: CC BY-NC 3.0

line graph shows how data changes over time. Here is an example.

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double line graph compares how two sets of data change over time. This example compares six sets of data.

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A pie chart shows a percentage out of a whole. Here is an example.

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So, if a girl scout sells 20 boxes of thin mints, 13 boxes of samoas, and 5 boxes of tagalongs a table showing this data would look like:

Thin Mints Samoas Tagalongs
Girl Scout 1 20 13 5

But if she wanted to represent her data in a visual way so that it was immediately clear which cookie sold the best, she would choose to display her data with a bar graph because number of cookie boxes sold is a type of frequency.

Now, if she wanted to compare her cookie sales to those of another girl scout, she would choose a double bar graph because that would immediately show the relative frequencies of the two.

Examples

Example 1

Earlier, you were given a problem about Rahul and his question about California rainfall.

He is trying to decide how best to display his data from the table below.

Season (July 1-June 30) (Year given represents end of season)

Inches Above/Below (+/-) 135 Year Average

2012

-6.29

2011

+5.22

2010

+1.38

2009

-5.90

2008

-1.45

2007

-11.77

2006

-1.79

2005

+22.98

2004

-5.73

2003

+1.44

2002

-10.56

2001

+2.96

2000

-3.41

1999

-5.89

1998

+16.03

1997

-2.58

1996

-2.54

1995

+9.37

1994

-6.87

1993

+12.38

1992

+6.02

1991

-2.99

1990

-7.63

1989

-6.90

1988

-2.50

1987

-7.32

1986

+2.88

1985

-2.16

1984

-4.55

1983

+16.3

1982

-4.27

1981

-6.02

1980

+12.00

1979

+4.69

1978

+18.46

1977

-2.68

1976

-7.77

1975

-0.63

1974

-0.06

1973

+6.28

1972

-7.81

1971

-2.66

1970

-7.24

1969

+12.49

1968

+1.60

1967

+7.02

1966

+5.46

1965

-1.30

1964

-7.05

1963

-6.60

First, he determines what type of data is given: frequency, change over time, or percentage of a whole.

In this case, it is change in rainfall over time. So it would best be described using a line graph.

Next, he determines how many lines of data there are.

He only has one rainfall value/year and his chart does not have any other type of data, so he concludes that a single line graph would be best.

Example 2

Determine which type of graph will best display the data below.

Keith gathered the following data about how bus fare changed in his town over a period of five years. He wants to bring it to the PTA to show that free bus passes ought to be given to students.

2007 .35

2008 .35

2009 .40

2010 .40

2011 .45

First, determine what type of data is given. Is the data a matter of frequency, change over time, or percentage of a whole?

In this case, it is change over time. So it would best be described using a line graph.

Next, determine whether there is just one set of data that needs to be shown or if there are multiple lines of data to compare.

In this case, there is just one bus fare, so a single line graph will suffice.

The answer is a single line graph.

Example 3

What graph would best show how often someone eats ice cream?

First, determine what type of data is given. Is the data a matter of frequency, change over time, or percentage of a whole?

In this case, the data is about frequency. So it would best be described using a bar graph.

Next, determine whether there is just one set of data that needs to be shown or if there are multiple lines of data to compare.

In this case, there is just one person eating ice cream, so a single bar graph will suffice.

The answer is a single bar graph.

Example 4

What graph would best describe how much of someone's monthly budget is allocated to rent, food, and other bills?

First, determine what type of data is given. Is the data a matter of frequency, change over time, or percentage of a whole?

In this case, it is the percentage of someone's entire budget. So it would best be described using circle graph.

The answer is a pie chart.

Example 5

What would be the best way to show that climate is changing over time?

First, determine what type of data is given. Is the data a matter of frequency, change over time, or percentage of a whole?

In this case, it is change over time. So it would best be described using a line graph.

Next, determine whether there is just one set of data that needs to be shown or if there are multiple lines of data to compare.

In this case, it would depend. You could just show that the temperature was raising over time. Or you could add on top of that other indicators like CO2 levels or levels of water melted in polar icecaps that have also changed over time.

So this data could be presented either with a single or multiple line graph.

Review

Select the best display for each description of data. Choose from circle graph, line graph, double line graph, bar graph or double bar graph.

  1. The percentages of people who enjoy ice cream
  2. How stamp prices have changed over time
  3. How stamp prices changed in 1996 and in 1998.
  4. The number of students who attended college in 1990, 1991, and 1992
  5. The percentages of people who prefer chocolate, vanilla or strawberry ice cream.
  6. The changes in prices at one movie theater over a period of three years.
  7. The changes in prices at two different movie theaters over a period of three years.
  8. A graph showing how sales had declined during the past month
  9. A graph showing the number of students with perfect attendance during the past three months.
  10. A graph showing the number of students with perfect attendance at two different schools during the past three months.
  11. The percentages of students who complete homework.
  12. The percentages of students who enjoy playing particular sports.
  13. How the percentages of students who attend college has changed over time.
  14. How the price of a hamburger has changed over time.
  15. The percentages of people who enjoy watching particular sports events.

Review (Answers)

To see the Review answers, open this PDF file and look for section 11.19. 

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Vocabulary

binning

Binning involves separating your data separated into separate classes or categories.

continuous variables

A continuous variable is a variable that takes on any value within the limits of the variable.

discrete random variables

Discrete random variables represent the number of distinct values that can be counted of an event.

relative frequency table

A relative frequency table is specifically designed to display the ratio of each individual frequency to the total frequency of the data.

Statistics

Statistics is a branch of mathematics that involves collecting, analyzing and displaying data.

Survey

A survey is a method of collecting data where you ask a sample of people the same question.

Image Attributions

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