23 Frequency Distributions and Graphs
Learning Objectives
- Create frequency and relative frequency distributions
- Create different types of graphs for data
Create Frequency and Relative Frequency Distributions
Both qualitative (categorical) and quantitative data can be arranged in frequency and relative frequency tables.
Frequency Table
A frequency table is a table with two columns. One column lists the outcome or the numeric range, and the second column lists the frequency (the number of items that are in that category or numeric range). When the first column contains a numeric range we call them classes.
Relative Frequency Table
A relative frequency table is a table with two columns. One column lists the outcome or the numeric range and the second column lists the relative frequency (the proportion of items in the category or numeric range).
Example 1: Frequency and Relative Frequency Tables.
A group of adults were asked how many children under the age of 18 they had living in their households. The data below represent their answers.
| 3 | 1 | 2 | 4 | 2 | 3 | 4 | 5 | 1 | 4 |
| 3 | 4 | 5 | 3 | 0 | 1 | 3 | 4 | 2 | 2 |
Create a Frequency and Relative Frequency table of the data and then compare your work with the table below. What do you notice about the sum of the numbers in the “Relative Frequency” column?
|
Number of Children |
Frequency |
Relative Frequency |
|
0 |
1 | 1/20 = 0.05 |
|
1 |
3 |
3/20 = 0.15 |
|
2 |
4 |
4/20 = 0.2 |
|
3 |
5 |
5/20 = 0.25 |
|
4 |
5 |
5/20 = 0.25 |
|
5 |
2 |
2/20 = 0.1 |
Example 2. Frequency and Relative Frequency Tables.
The following data represent the numeric scores of a math class on the final.
| 75 | 86 | 56 | 83 | 66 | 58 | 57 | 98 | 68 | 70 |
| 51 | 97 | 73 | 78 | 89 | 57 | 67 | 70 | 61 | 75 |
Create a Frequency and Relative Frequency table of the data and then compare your work with the table below. What do you notice about the sum of the numbers in the “Relative Frequency” column?
|
Test Score (or Bin) |
Frequency |
Relative Frequency |
|
50-59 or [50, 60) |
5 |
5/20= 0.25 |
|
60-69 or [60, 70) |
4 |
4/20= 0.2 |
|
70- 79 or [70, 80) |
6 |
6/20= 0.3 |
|
80- 89 or [80, 90) |
3 |
3/20= 0.15 |
|
90- 99 or [90, 100] |
2 |
2/20= 0.1 |
Create Different Types of Graphs for Data
Bar Graphs
A bar graph is constructed by labeling each outcome of the data on the horizontal axis and the frequency or relative frequency on the vertical axis. Then for each category, draw a rectangle whose height is the frequency or relative frequency. Bar graphs are used with categorical (or qualitative) data.
Example 3. Bar Graphs
Create a frequency bar graph from the following data.
The table below is a frequency table of the letter grades students received in a calculus class last semester.
|
Letter Grade |
Frequency |
Relative Frequency |
|
A |
6 |
0.273 |
|
B |
7 |
0.318 |
|
C |
4 |
0.182 |
|
D |
3 |
0.136 |
|
F |
2 |
0.091 |
Bar Graph of Letter Grades in Calculus**
**The vertical axis should be labeled “Frequency.” The horizontal axis is labeled with the grade. Notice that a bar graph is when our outcomes are categories or qualitative data.
Pie Charts
A pie chart is a circle with wedges cut of varying sizes marked out like slices of pie or pizza. The relative sizes of the wedges correspond to the relative frequencies of the categories
Example 4. Pie Chart
Create a pie chart for the relative frequencies for the given data.
|
Letter Grade |
Frequency |
Relative Frequency |
|
A |
6 |
0.273 |
|
B |
7 |
0.318 |
|
C |
4 |
0.182 |
|
D |
3 |
0.136 |
|
F |
2 |
0.091 |
Pie Chart of Letter Grades in Calculus
Notice how the size each slice (or the proportion of the “pie” a slice takes up) is the same as the relative frequency of that grade.
Histogram
A histogram is constructed like a bar graph except that the categories are bins of quantitative (or numerical) data.
A histogram is constructed by creating “bins” of quantitative data on the horizontal axis and the frequency or relative frequency of the amount of data in each bin on the vertical axis. Then for each bin, draw a rectangle whose height is the frequency or relative frequency. histograms are used with quantitative (or numerical) data.
Example: Create a histogram using the frequency from the frequency table below.
|
Test Score (or Bin) |
Frequency |
Relative Frequency |
|
50-59 or [50, 60) |
5 |
0.25 |
|
60-69 or [60, 70) |
4 |
0.20 |
|
70- 79 or [70, 80) |
6 |
0.30 |
|
80- 89 or [80, 90) |
3 |
0.15 |
|
90- 99 or [90, 100] |
2 |
0.10 |
Attributions
- Content and structure adapted from:
- RSCC Math 1410/1420 OER Team, 2022, CC BY 4.0.
- Portions of this content adapted from ‘Math in Society Edition 2.5’ by David Lippman: Statistics (http://www.opentextbookstore.com/mathinsociety/2.5/Sets.pdf) and Describing Data (http://www.opentextbookstore.com/mathinsociety/2.5/DescribingData.pdf). Data gathered from State of TN: June 2020 Election Statistics (https://sos.tn.gov/products/elections/election-statistics).
Media Attributions
- Bar graph- Grades
- Grades pie
- Histogram example
