Important terminology:

Frequency distribution	A table of data values and corresponding frequencies.
Frequency	The number of data points that fall within a class, or range of data points.
Class	Levels or categories used to explain the spread of a data list
Lower class limit (LCL)	Smallest whole number boundary of a class
Upper class limit (UCL)	Largest whole number boundary of a class
Class boundary	The space between the gap of each class limit
Class midpoints	The median of each class (add the lower class limit and the upper class limit and divide by 2)
Class width	The distance between each consecutive lower class limit (the highest value minus the lowest value divided by the number of classes)

 

How to make a frequency distribution:

1.    Decide how many classes you want to have

2.    Find the class width and round the number (most of the time you round this number up)

3.    Find the lowest data value in the data set, this will be the lowest class limit

4.    Add the class with to the lowest class limit (from step 3). This is the second class’ lower limit.

5.    Repeat step 4 until you exceed the highest value in the data set.

6.    Find the upper class limits, add one minus the class width to each lower limit

7.    Fill out the class section of the frequency distribution (the table below).

8.    Find the class frequencies (number of values that fall within each class).

 

Relative frequency distributions:

9.    Divide each class frequency by the sum of all frequencies.

 

Cumulative frequency distributions:

9.  Using the upper class limits, at each limit add all frequencies below the upper class limit

 

EXAMPLE 1:

 

I recently asked several tutors what their GPAs were, and got the following GPAs: 3.4, 3.7, 3.0, 3.9, 3.4, 3.1, 3.5, 3.8, 3.0, 3.5, 3.4, 3.4, 3.9, 3.8, 3.9, 3.2, 3.2

 

If I want to show the info in a frequency distribution. I’d follow these steps:

 

1.    Decide how many classes you want to have

 

I want to have 5 classes

 

2.    Find the class width and round the number (most of the time you round this number up)

 

Class width: (3.9-3.0) / 5 = 0.18 ≈ 0.2

 

3.    Find the lowest data value in the data set, this will be the lowest class limit

 

3.0 is the lowest class limit

 

4.    Add the class width to the lowest class limit (from step 3). This is the second class’ lower limit.

 

3.0 + 0.2 = 3.2

 

5.    Repeat step 4 until you exceed the highest value in the data set.

 

Lower Class Limit

3.0

3.0 +0.2 = 3.2

3.2 +0.2 = 3.4

3.4 +0.2 = 3.6

3.6 +0.2 = 3.8

3.8 +0.2 = 4.0

 

6.    Find the upper class limits, typically one minus the class width to each lower limit.

Lower Class Limit	Upper Class Limit
3.0	3.2 - 0.1 = 3.1
3.0 +0.2 = 3.2	3.4 - 0.1 = 3.3
3.2 +0.2 = 3.4	3.6 - 0.1 = 3.5
3.4 +0.2 = 3.6	3.8 - 0.1 = 3.7
3.6 +0.2 = 3.8	4.0 - 0.1 = 3.9

7.    Fill out the class section of the frequency distribution (the table below).

 

Classes
Lower Class Limit	Upper Class Limit
3	3.1
3.2	3.3
3.4	3.5
3.6	3.7
3.8	3.9

 

 

8.    Find the class frequencies (number of values that fall within each class).

 

Classes		Counts	Frequency
Lower Class Limit	Upper Class Limit
3	3.1	|||	3
3.2	3.3	||	2
3.4	3.5	||||||	6
3.6	3.7	|	1
3.8	3.9	|||||	5

 

Relative frequency distributions, follow steps 1-8 above and:

9.    Divide each class frequency by the sum of all frequencies.

           

Relative frequency distribution:

 

Classes		Frequency	Relative Frequency
Lower Class Limit	Upper Class Limit
3	3.1	3	3/17 =	0.18
3.2	3.3	2	2/17 =	0.12
3.4	3.5	6	6/17 =	0.35
3.6	3.7	1	1/17 =	0.06
3.8	3.9	5	5/17 =	0.29
TOTAL		17		1.00

 

Cumulative frequency distributions, follow steps 1-8 above and:

 

    9. Using the upper class limits, at each limit add all frequencies below the

        Upper Class Limit (see below)

 

Classes		Frequency	Class	Cumulative frequency
Lower Class Limit	Upper Class Limit		Less than 3.0		0
3	3.1	3	Less than 3.2		3
3.2	3.3	2	Less than 3.4	3+2=	5
3.4	3.5	6	Less than 3.6	3+2+6=	11
3.6	3.7	1	Less than 3.8	3+2+6+1=	12
3.8	3.9	5	Less than 4.0	3+2+6+1+5=	17