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: Categories in first column Numbers in second column Do the categories add up to a whole (in this case the whole class)? Do the categories overlap? Do the numbers add up to a whole, either 100% or a total number? 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, let’s 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? 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. 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%)? 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: 39,483+145,569 = 185,052Check: 598+1,799+17,302+19,784 = 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 _________.” 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. 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. 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? 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? 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. 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. It’s that simple. It’s that simple.

10. Pie Graphs Versus Column Graphs Pie graphs are used for numbers associated with categories, Pie graphs are used for numbers associated with categories, when both the numbers and the categories add up to a whole. when both the numbers and the categories add up to a whole. Pie chart data always represents data from a single year or time. Pie chart data always represents data from a single year or time. Column graphs are also used for numbers associated with categories, but 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. 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. 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: One set of categories A second set of categories A blank space Select all of this!

13. III. x-y scatter plots An x-y scatter plot is a way of graphing data that changes over time 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). 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.). 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. 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 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. 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 don’t 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 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 Note: All data is in thousands

16. How might we describe this graph using language? The crime rate is… Increasing Increasing Leveling off Leveling off Decreasing Decreasing Leveling off Leveling off Decreasing Decreasing We might also notice when the highest and lowest points occurred… In 1991-92 there were 758 crimes per 100,000 people In 1991-92 there were 758 crimes per 100,000 people In 2003, there were 475 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: In the early 90’s 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 90’s 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. 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.