Types of Graphs Line plots, bar graphs, histograms, stem and leaf plots and box plots (box and whisker)
Graphs are pictures of different kinds of data shown on number lines. Before you can make a graph of any kind, you must first collect or have a set of information called data. One of the best and easiest ways to collect this data is in a Frequency Table.
A frequency table is best used when data can be divided into intervals. Most of the time the definition of interval is something like this: "The number of units between spaces on a graph's scale." Unfortunately, this doesn't help much. Let's see if we can work towards a good understanding.
Pretend this is a class seating chart, only instead of names, we have the color of shirts each student is wearing. We would use one form of frequency table to collect this data.
| Shirt color | Tally | Frequency |
| black | ||| | 3 |
| blue | |||||| | 6 |
| gray | |||||| | 6 |
| green | |||| | 4 |
| red | |||| | 4 |
| white | ||| | 3 |
| yellow | || | 2 |
In this kind of Frequency Table, the interval is determined by the shirt color. This is the easiest kind of interval -- when it is the name of something specific.
Student height in cm |
157 152 164 150 166 166 148 159 156 149 162 157 159 153 158 159 141 164 168 153 158 151 143 177 168 157 157 167 |
Here we have the same class seating chart, only this time we have the height of the students in centimeters instead of shirt colors. If you look at the information carefully, you will see that the shortest student is 141cm and the tallest is 177cm. we could make a frequency table that had intervals (or steps) of 1cm. However, that kind of information would be better presented on a line plot. What we are looking for in a frequency table is a way to gather or group data so we can make a picture of the results that is easy to see. Here are the steps to follow:
- Determine the scale. The scale is a range of numbers that includes the smallest and the largest. In this case, the actual numbers range from 141 to 177 (a range of 36) so we could pick a scale of 140 to 180. (remember it has to include all the numbers)
- After we have a scale we need to decide how we are going to divide the scale into equal parts - these equal parts are called intervals. Since our scale is 140 to 180 in this case, it looks like it would divide nicely into groups of 10.
- This is important! Be sure that you do not have overlapping numbers. This means, be sure that you do not have the same number in two places.
- Set up your frequency table (use a ruler
) with three colums: Intervals then Tally then Frequency. The Tally column is where you make your counting mark to detemine how many numbers you have in that interval. The Frequency column is the number count of the tally (look back at the short color information)
Here is our Frequency table for the class heights:
|
Height Intervals |
Tally | Frequency |
| 141-150 | |||| | 4 |
| 151-160 | ||||| ||||| ||||| | 15 |
| 161-170 | ||||| ||| | 8 |
| 171-180 | | | 1 |
Always check to make sure your numbers add up to the number of c\pieces of data you have. This class has 28 student present when the information was collected.
Here is some more information: Tables and Graphs
Now that we have our data we can display it in different ways. Please remember that there are many different ways to show the information. You as the presenter have a choice.
Graphic Presentation - Line Plot
A line plot is a graphic show of data on a number line. (Do not confuse Line PLOTS with Line GRAPHS.)
[
Line Plots]
[Line Plots - More information]
Graphic Presentation - Bar Graph
Bar graphs are used when the data is non-continuous. Non-Continuous means that the information is not the next step, or continuation of the information before it. For example, in the shirt graph below, the colors are separate pieces of information - they do not have to go in any particular order - you could put the green where the black is, etc.
[Bar Graphs]
[More Bar Graphs]
Graphic Presentation - Histogram
Histograms are like bar graphs except the data is continuous which means that the data before and after a particular bar are in order. As a result, there are no spaces between the bars!
[Histogram]
Graphic Presentation - Stem and Leaf Plot
Stem and Leaf plots are another way to present data. They get their name from their sort-of resemblence to tree branches. We can make a stem and leaf plot from the class height data. The first thing we have to do is find out what is the stem and what are the leaves. The data for the heights is listed in centimeters. They rannge from 141 to 177 centimeters. The way a stem and leaf plot works is you take the number in the right-most position and those numbers are the leaves. The remainder of the number is the stem.
157 152 164 150 166 166
148 159 156 149 162 157
159 153 158 159 141 164
168 153 158 151 143 177
168 157 157 167
For this data, the leaf is the numeral in the ones place - the rest of the number makes up the stem.
Line up the stems vertically, draw a line next to them. Now go through the list of data and put each 'leaf' next to its stem. This is the first sort. Next, arrange the leafs from the stem out in numerical order (0 close to the stem; 9 farthest out.
Be sure to put a key with your stem and leaf plot.
[Stem and Leaf Plot]
[More Stem and Leaf Plot]
Graphic Presentation - Box Plot (Box and Whisker)
This is a box plot of the class height data. Box plots require more math then other types of plots. The most im[portant process you need to use is to find the median of data.
To find the median:
1 2 3 4 5 3 is the median 1 2 3 4 5 6
3 + 4 = 7 ÷ 2 = 3.5 is the median |
To make a successful box plot you need the following items:
- Lower Exteme - the smallest value in your list (141cm on this plot)
- Lower Quartile - the median of the lower half of the data (152.5cm)
- Median - the mid-point of the data in order (157.5cm)
- Upper Quartile - the median of the upper half of the data (164)
- Upper Extreme - the greatest value in your date (177cm)
[Box Plot - box and whisker]
[Box Plot]