Describing Data Graphically

Sometimes the best way to describe data is by using tables and graphs. Tables and graphs give you a quick way to visualize the entire data set, without reducing it down to just a few descriptive numbers. There are different ways to describe categorical data versus numerical data.

Categorical Displays:

Pie chart: This type of graph displays a wedge for each category of responses. This type of chart is best used when there are only a few types of categories. In order to draw a pie chart, you must first calculate a category's relative frequency and multiply that by 360°. Why 360°? Because a pie chart is drawn using a circle and there are 360° in a circle.

Bar chart (also called a comparative bar chart): This type of graph shows the Relative Frequency of a category along a single axis, and it is often paired with a second group of categories.


Dot plot: This is a very simple statistical plot that uses a dot to show every occurrence in a category.

This dotplot shows that it generally did not rain more than 0.05 inches in any given 15 minutes, but there was at least one time when 0.09 inches of rain fell within 15 minutes. It also shows you that it was quite common for it to not rain at all -- notice that the most frequent measurement was 0.00 in.

Numerical Displays:
Stem Plot (also called a stem-and-leaf plot): This type of graph is a concise way to show all of the data. Each number is broken up into a stem and a leaf. Where the break is depends on the data set. For example, a data set that consists of all 4-digit numbers might be broken up like this: 9000 is 9- stem, 000-leaf. While a data set comprised entirely of 3 digit numbers all in the 100’s, it might be broken up like this: 110 is 11- stem, and 0 leaf.

In this plot you can quickly see that the patients tend to be older, and you can see the exact age of the patients. No summarizing was done -- only organization.

Histogram:

While a histogram looks similar to a bar chart, it lumps data into numerical bins instead of categories. This type of graph shows you the frequency, the number of times something occurs, of a numerical data set.  (Notice this is different than relative frequency.)

Example:

The length was measured on all Largemouth bass captured in a lake, and the number of fish that were between 10 and 11 inches was the most common length. That occurred approximately 46 times.

Cumulative Frequency plot
This type of graph shows you the frequency of this occurring in a particular bin, along with all of the bins to the left.

Example:
You want to know the percentage of fish that are 15 inches or less, and we could easily read this number off a relative cumulative frequency graph -- 86%.

Practice:
State which graph you would use in each of the circumstances below, and explain why this is the best graph to use.
  1. You want to compare how much money you spent in 4 different categories 
  2. You want to compare how much money you and your husband spent in 4 different categories. 
  3. You want to be able to see at a quick glance every dollar amount you spent 
  4. You want to see how many times you spent money in 4 different categories. 
  5. You want to know the frequency of the amounts of money that you spend. 
  6. You want to see how quickly you spent all of your money. 
Answers:
  1. Pie chart. Each wedge of the pie will be equal to the relative frequency of each category so that you can quickly compare categories. 
  2. Bar Chart. Each category will be split in half to compare a husband and wife’s spending. 
  3. Stem-and-leaf plot. This will show all amounts spent, making it easy to see if purchases are large or small, and it shows every purchase amount.
  4. Dot plot. This will show whether you are making a few large purchases or many small purchases in a category 
  5. Histogram. This will show how common your purchase amounts are. Do you make a lot of small purchases or a few large purchases? 
  6. Cumulative frequency, the steepness of the accumulation of money spent will show you whether you spend your money on large purchases (steeper) or small purchases (less steep). 
References:

Crawley MJ. 2007. The R Book. West Sussex, England: John Wiley & Sons

Lohr SL. 1999. Sampling: Design and Analysis. Pacific Grove, CA: Brooks/Cole.

Peck R, Olsen C, Devore JL. 2012. Introduction to Statistics and Data Analysis. Boston: Brooks/ Cole. 912 p.

Ramsey FL, Schafer DW. 2012. The Statistical Sleuth: A Course in Methods of Data Analysis, 3rd ed.: A Course in Methods of Data Analysis: Brooks/Cole, Cengage Learning.

http://nwis.waterdata.usgs.gov/nv/nwis/uv?

Large mouth Bass data our my own data