Making Effective Pie Graphs, Bar/Column Graphs and X-Y Scatter graphs

1
Making Effective Pie Graphs, Bar/Column Graphs
and X-Y Scatter graphs
2
I. A pie graph
is a graph that represents exactly one whole or
100 of something.
The pieces of the pie, therefore, must 1.) Add
up to exactly one whole. and 2.) Be distinct (in
other words they must not overlap).
3
Arranging the data for a pie chart
Numbers in second column
Categories in first column
Do the numbers add up to a whole, either 100 or
a total number?
Do the categories add up to a whole (in this case
the whole class)? Do the categories overlap?
To make a pie chart select both the categories
and the data.
4
What is wrong with the following graphs?
The categories overlap for example, a student
in the class could be both a woman and black.
The categories add up to two wholes, not one.
Violent crime includes all murders, robberies
and assaults, so every violent crime is accounted
for twice on this chart.
5
So, to correctly make or analyze a pie graph you
must ask yourself the following key questions
1.) What is the whole? 2.) Do the categories add
up to this whole? 3.) Do the categories overlap?
(In other words, would it be possible for
something to be counted in more than one of the
categories being used?)
In order to practice this, lets look at some
real data from the Statistical Abstract.
6
How to tell from a data set if a pie chart is an
appropriate choice

• Are the numbers total counts, and do they add
  up to form a natural whole?
• Any set of total counts can be used, but remember
  the whole will always be the sum of the
  individual categories.
• Or, are the numbers in percentage form, and do
  they add up to 100 (or approximately 100)?

7
Find three examples of a whole and state the
categories that could comprise each of these
wholes.
Check 39,483145,569 185,052
Check 5981,79917,30219,784 39,483
8
How to tell from a question if the answer is a
pie chart

• Find the part of the question or statement that
  reads the percentage of _________.
• Whatever is in the place of the blank is the
  whole. If there is only one whole being referred
  to then likely the question is talking about pie
  chart data.
• If there is more than one whole, then the data
  will likely have to be represented by a bar
  graph.
• Examples What percentage of women and what
  percentage of men claim that chocolate is their
  favorite flavor?
• What percent of all chocolate lovers are male and
  what percent are female?

9
II. Making a column graph

• Select the data just as you would for a pie
  chart, but when you choose the type of graph you
  want to make, choose Column or Bar graph
  instead.
• Its that simple.

10
Pie Graphs Versus Column Graphs

• Pie graphs are used for numbers associated with
  categories,
• when both the numbers and the categories add up
  to a whole.
• Pie chart data always represents data from a
  single year or time.

• Column graphs are also used for numbers
  associated with categories, but
• the data for a column graph may or may not add up
  to a whole.
• Multiple column graphs can compare data from
  different years. We will look at this type of
  graph in the next class.

11
A multiple column/bar graph is
used to show comparisons between two categories.
In this case it is types of crime and the year.
It is still important to know the whole to which
the percentages refer.
It is clear here that the whole is all crime
since violent crime (73) property crime
(27) all crime (100)
12
Arranging the data for a multiple column/bar
chart
A second set of categories
A blank space
Select all of this!
One set of categories
13
III. x-y scatter plots

• An x-y scatter plot is a way of graphing data
  that changes over time
• Or, more generally, any data that is of the form
  (a number, a number).
• But, in this class, virtually all of the x-y
  scatter plots you look at will be something that
  changes over time (abortion rate, population,
  poverty line, the price of stamps, etc.).
• So, the x-axis will be years, and the y-axis will
  be the quantity that is changing.
• When possible, use relative rather than absolute
  numbers.
• When labeling the x and y-axis and giving the
  chart a title, make sure you know the units and
  the whole to which percents (if you are using
  percents) refer.

14
Here are the violent crime statistics (in
thousands) for the United States since 1990
Why is this NOT a very interesting graph?
These are total numbers. We dont know what these
numbers mean relative to the population of the
U.S..
15
To fix the problem, get the population for each
of these years
Note All data is in thousands
and then compute total crimes/total population
to get the crime rate.
For example in 1990, (1,820 thousand
crimes)/(249,470 thousand people) .00703 OR
703 crimes per 100,000 people
16
How might we describe this graph using language?

• The crime rate is
• Increasing
• Leveling off
• Decreasing
• Leveling off
• Decreasing

• We might also notice when the highest and lowest
  points occurred
• In 1991-92 there were 758 crimes per 100,000
  people
• In 2003, there were 475 crimes per 100,000 people

17
Putting this altogether, we could describe the
graph as follows
The goal in this sort of description is to 1.)
Give a good idea of overall trends, and 2.) Point
out the most interesting or surprising features.
In the early 90s crime rates were still rising
in the United States, but they peaked in 1992 at
758 crimes per 100,000 people. Through the mid
to late 90s there was a decline in the crime
rate, bringing it to a low-point of 475 crimes
per 100,000 people in 2003. But, we may have
some cause for concern because although the crime
rate has continued to decrease, it seems to have
leveled off after the turn of the millennium.