2.3 Displaying Quantitative Data
Descriptive Statistics for Quantitative Data
Descriptive options for quantitative data are much more robust than for categorical. Recall descriptive statistics consists of visual and numerical methods. We usually start with visual methods and then move into numerical.
This section will expand on graphical methods while the next few sections will focus on numerical summaries of quantitative data.
Graphical Methods for Quantitative Data
The first thing we may do, especially for quantitative data, is to examine it in a frequency table. We have many more graphical options beyond that for quantitative data. Some of them we will discuss here are:
- Stem-and-leaf plots
- Dot plots
- Line graphs
- Histograms
- Frequency polygons
- Time series plots
Each of these methods comes with it’s own pros and cons.
Stem-And-Leaf Plots
One simple graph, the stem-and-leaf graph or stemplot, comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a “stem” and a “leaf”. The leaf consists of a final significant digit. For example you could divide the number 23 into a stem two and a leaf of three. The number 432 could have a stem of 43 and leaf of two. The decimal 9.3 could have a stem of nine and leaf of three. Write the stems in a vertical line from smallest to largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem.
Example
For Susan Dean’s spring pre-calculus class, scores for the first exam were as follows (smallest to largest):
33, 42, 49, 49, 53, 55, 55, 61, 63, 67, 68, 68, 69, 69, 72, 73, 74, 78, 80, 83, 88, 88, 88, 90, 92, 94, 94, 94, 94, 96, 100
| Stem | Leaf |
|---|---|
| 3 | 3 |
| 4 | 2 9 9 |
| 5 | 3 5 5 |
| 6 | 1 3 7 8 8 9 9 |
| 7 | 2 3 4 8 |
| 8 | 0 3 8 8 8 |
| 9 | 0 2 4 4 4 4 6 |
| 10 | 0 |
The stemplot shows that most scores fell in the 60s, 70s, 80s, and 90s. Eight out of the 31 scores or approximately 26% were in the 90s or 100, a fairly high number of As.
Comparisons with Stem-and-Leaf Plots
Back-to-back or side-by-side stem-and-leaf plot allows a comparison of the two data sets in two columns. In a side-by-side stem-and-leaf plot, two sets of leaves share the same stem. The leaves are to the left and the right of the stems.
Your turn!
The following two tables show the ages of U.S. presidents at their inauguration and at their death. Construct a side-by-side stem-and-leaf plot using this data.
| President | Age | President | Age | President | Age | President | Age |
|---|---|---|---|---|---|---|---|
| Washington | 57 | Fillmore | 50 | McKinley | 54 | Nixon | 56 |
| J. Adams | 61 | Pierce | 48 | T. Roosevelt | 42 | Ford | 61 |
| Jefferson | 57 | Buchanan | 65 | Taft | 51 | Carter | 52 |
| Madison | 57 | Lincoln | 52 | Wilson | 56 | Reagan | 69 |
| Monroe | 58 | A. Johnson | 56 | Harding | 55 | G.H.W. Bush | 64 |
| J. Q. Adams | 57 | Grant | 46 |