Lesson 142:  Working with Frequency Tables

In this easy lesson we'll look at how to create and use a frequency table.  These tables come up very frequently (no pun intended) in statistical work.

Very often we are given a long list of numbers, perhaps test scores, and we are asked to do different things with that list.  We might be asked to find the mean, median, or mode.  We might be asked to find the lower quartile, or what percentile corresponds to a particular score.  We learned how to do all these things, but all of these things are more easily done if we put the data into a frequency table.  Sometimes a problem will tell us specifically to do that. 

Here is a long list of test scores:  14, 17, 28, 28, 30, 36, 45, 52, 58, 58, 61, 64, 64, 68, 68, 77, 77, 81, 81, 81, 81, 87, 87, 94, 94, 95, 95, 95, 95, 95, 95, 97, 97, 97, 100, 100

Let's make a frequency table for this data.  That will show us all the scores, and how often each one occurs.  We'll make a column for the scores, a column in which we can use tick marks to tally up each score, and then a column that shows the number of occurrences (frequency) for each score.  Then we'll add a row at the bottom for the total scores. 

Score	Tally	Frequency
14	|	1
17	|	1
28	||	2
30	|	1
36	|	1
45	|	1
52	|	1
58	||	2
61	|	1
64	||	2
68	||	2
77	||	2
81	||||	4
87	||	2
94	||	2
95	|||| |	6
97	|||	3
100	||	2
Total:		36

Notice how we use the tick marks.  For frequencies of 1-4, we just use a vertical line for each occurrence.  Once we hit 5, we put a horizontal line through the group of 4.  That makes it easy to count by fives. 

Sometimes you'll be asked to make a frequency table for specific intervals.  In some cases, the data is more meaningful that way, although it does not show you specific scores.  For example, let's make a table for the same data, but breaking down the scores into ranges of 10.  For this table, we'll omit the tick marks, but you could put them in if it helps you:

Interval	Frequency
0-10	0
11-20	2
21-30	3
31-40	1
41-50	1
51-60	3
61-70	5
71-80	2
81-90	6
91-100	13
Total	36

Sometimes you'll be asked to make a cumulative frequency table.  Each range includes the total scores that are at that level, or below.  "Cumulative" means accumulating.  In this case, we'll be able to see how many students scored at, or below a certain score:

Interval	Cumulative Frequency
0-10	0
0-20	2
0-30	5
0-40	6
0-50	7
0-60	10
0-70	15
0-80	17
0-90	23
0-100	36
Total	36

Remember that you can ask a math question if you have additional questions about a topic, or you can contact me if you have any comments or suggestions for this site.

Go to Next Lesson

Return to Free Math Lessons (141-160)

Site Last Updated on January 13, 2012

Copyright © 2011 MathWithLarry.com. All Rights Reserved.  Content may not be reproduced elsewhere.
Cary, NC 27513.  Mailing address available upon request.  Larry@MathWithLarry.com