• Summarizing qualitative data
• Summarizing quantitative data

• The frequency distribution
• The relative frequency distribution
• The percent frequency distribution
• The pie graph
• The bar graph

A frequency distribution is a tabular summary of data showing the frequency (or number) of items in each of several nonoverlapping classes.
The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data.

Marada Inn Example
Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent , above average , average , below average , or poor . The ratings provided by a sample of 20 guests are :
Below Average
Above Average
Above Average
Average
Above Average
Average
Above Average
Average Above Average
Above Average Above Average
Below Average Below Average
Poor Poor
Excellent Above Average
Above Average Average
Average Average

Poor
Rating
Below Average
Average
Above Average
Excellent 1
Total 20
5
9
2
3

Using Excel’s COUNTIF function to construct a frequency distribution
Formula Worksheet
A
1 Quality Rating
2 Above Average
3 Below Average
4 Above Average
5 Average
6 Average
7 Above Average
8 Above Average
B C D
Quality Rating Frequency
Poor =COUNTIF($A$2:$A$21,C2)
Below Average =COUNTIF($A$2:$A$21,C3)
Average =COUNTIF($A$2:$A$21,C4)
Above Average =COUNTIF($A$2:$A$21,C5)
Excellent =COUNTIF($A$2:$A$21,C6)
Total =SUM(D2:D6)
Rows 9-21 not shown

• The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class.
• A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class.

• The percent frequency of a class is the relative frequency multiplied by
100.
• A percent frequency distribution is a tabular summary of a set of data showing the percent frequency for each class.

Using Excel’s COUNTIF function to construct a frequency distribution
Value Worksheet
A
1 Quality Rating
2 Above Average
3 Below Average
4 Above Average
5 Average
6 Average
7 Above Average
8 Above Average
B C
Quality Rating Frequency
Poor 2
Below Average 3
Average 5
Above Average 9
Excellent 1
Total 20
D
Rows 9-21 not shown

Relative Frequency and
Percent Frequency Distributions
Rating
Relative
Frequency
Poor
Below Average
Average
Above Average
Excellent
Total
.10
.15
.25
.45
.05
1.00
Percent
Frequency
10
15
25
45
5
100
.10(100) = 10
1/20 = .05

Using Excel’s COUNTIF function to construct a percent frequency distribution
Formula Worksheet
C D E
Relative
Frequency 1 Quality Rating Frequency
2 Poor =COUNTIF($A$2:$A$21,C2) =D2/$D$7
3 Below Average =COUNTIF($A$2:$A$21,C3) =D3/$D$7
4 Average =COUNTIF($A$2:$A$21,C4) =D4/$D$7
F
Percent
Frequency
=E2*100
=E3*100
=E4*100
7
8
5 Above Average =COUNTIF($A$2:$A$21,C5) =D5/$D$7
6 Excellent =COUNTIF($A$2:$A$21,C6) =D6/$D$7
Total =SUM(D2:D6)
=E5*100
=E6*100
=SUM(E2:E6) =SUM(F2:F6)
Rows 9-21 and columns
A-B are not shown

Using Excel’s COUNTIF function to construct a percent frequency distribution
Value Worksheet
C D
1 Quality Rating
2 Poor
3 Below Average
4 Average
7
8
5 Above Average
6 Excellent
Total
Rows 9-21 and columns
A-B are not shown
Frequency
2
3
5
9
1
20
E
Relative
Frequency
0.10
0.15
0.25
0.45
0.05
1.00
F
Percent
Frequency
10
15
25
45
5
100

•These are used to display qualitative data.
•On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes.
•A frequency , relative frequency , or percent frequency scale can be used for the other axis (usually the vertical axis).

Bar Graph
Marada Inn Quality Ratings
10
9
8
7
6
5
4
3
2
1
The bars are separated to emphasize the fact that each class is a separate category.
Poor Below
Average
Average Above
Average
Excellent
Rating

Using Excel’s Chart Wizard to Construct Bar Graphs
S tep 1 Select cells C1:D6
Step 2 Click the Chart Wizard button
Step 3 When the Chart Type dialog box appears:
Choose Column in the Chart type list
Choose Clustered Column from the Chart
sub-type display
Click Next >
Step 4 When the Chart Source Data dialog box appears
Click Next >
… continued

Using Excel’s Chart Wizard to Construct Bar Graphs
Step 5 When the Chart Options dialog box appears:
Select the Titles tab and then
Type Marada Inn Quality Ratings in the
Chart title box
Type Quality Rating in the Value (X) axis box
Type Frequency in the Value (Y) axis box
Select the Legend tab and then
Remove the check in the Show Legend box
Click Next >
… continued

Using Excel’s Chart Wizard to Construct Bar Graphs
Step 6 When the Chart Location dialog box appears:
Specify the location for the new chart
Click Finish to display the bar graph

15
16
17
18
19
20
21
9
10
11
12
13
14
Using Excel’s Chart Wizard to Construct Bar Graphs
10
8
6
4
2
0
C D
Marada Inn Quality Ratings
Poor
E
Below
Average
Average Above
Average
Quality Rating
Excellent

Soft Drink Demonstration
Bar Graph of Soft Drink Purchases
20
15
10
5
0
Coke
Classic
Diet Coke Pepsi-Cola Dr. Pepper
Soft Drink
Sprite
Note: Excel file contained on text CD (Chapter 2--Softdrink



 The pie chart is a commonly used graphical device for presenting relative frequency distributions for qualitative data.
First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class.
Since there are 360 degrees in a circle, a class with a relative frequency of .25 would consume .25(360) = 90 degrees of the circle.

Pie Chart
Marada Inn Quality Ratings
Excellent
5%
Above
Average
45%
Poor
10%
Below
Average
15%
Average
25%

Soft Drink Demonstration
Soft Drink Frequency Distribution
Dr. Pepper
10%
Sprite
10%
Pepsi-Cola
26%
Coke Classic
Diet Coke
16%
38%
Note: Excel file contained on text CD (Chapter 2--Softdrink