1. Chapter 2 Describing Data Basic Statistics for Business and Economics
Fifth Edition
Chapter 2
Describing Data
Frequency distributions and Graphic Presentation
Douglas William Samuel
Irwin/McGraw-Hill 1 1 1 2 1 1

2. Topics Covered Organizing data in Frequency distributions
Frequency distributions types; histogram, frequency polygon, and cumulative frequency polygon.
Graphical techniques ; Line Charts, Bar Charts, and Pie Charts. 2 2 2 2 3 2

3. Constructing Frequency Distribution
The objective is to organize data in various ways to point out :
Where the data values tend to concentrate?
Distinguish the largest and smallest values.
Frequency distribution: grouping data into mutually exclusive classes showing the number of observations in each . 2 2 2 2 3 2

4. Constructing Frequency Distribution
There are five steps to organize data into frequency distribution;
1- Decide on the number of the classes
2- Determine the class interval or width
3- Set the individual class limits
4- Tally the data into the classes
5- Count the number of each item in each class. 2 2 2 2 3 2

5. Constructing Frequency Distribution
Example;
In the Text book, page 25, Ms Kathryn Ball of AutoUSA wants to develop some tables, charts, and graphs from the following raw materials, to show the typical selling price on various dealer lots.
Table 2-1 price vehicles sold last month at whitner Autoplex 2 2 2 2 3 2

6. Constructing Frequency Distribution
1- Decide on the number of the classes; The goal is to use just enough classes to revel the shape of distribution.
We use the formula;
> n K = number of classes
n = number of observations
(80 cars in our example)
If we try K =6 , then the answer will be 64 < 80
If we try K= 7, the answer will be 128 > 80
The best number of the classes will be 7 2 2 2 2 3 2

7. Constructing Frequency Distribution
2- Determine the class interval or width
First, we should find the highest observed value, and the lowest observed value.
Second, apply the formula;
i ≥ H – L i = Interval or width
k H= High amount
L = Low amount
k = number of classes
i = $35,925 – 15,546 = $2,911 7
So we use $3000 as the multiple of 10 or 100 2 2 2 2 3 2

8. Constructing Frequency Distribution
3- Set the individual class limits
State clear class limits so you can put each observation into only one category
Class
$15000 up to 18000
$18000 up to 21000
$21000 up to 24000
$24000 up to 27000
$27000 up to 30000
$30000 up to 33000
$33000 up to 36000 2 2 2 2 3 2

9. Constructing Frequency Distribution
4- Tally the data into the classes
State clear class limits so you can put each observation into only one category
Class Tallies
$15000 up to IIII III
$18000 up to IIII IIII IIII IIII III
$21000 up to IIII IIII IIII II
$24000 up to IIII IIII IIII III
$27000 up to IIII III
$30000 up to IIII
$33000 up to II 2 2 2 2 3 2

10. Constructing Frequency Distribution
5- Count the number of each item in each class
The number of observation in each class is called; class frequency.
Selling price Frequency
($ thousands) $ $ $ $ $ $ $
Total 2 2 2 2 3 2

11. Constructing Frequency Distribution
Class Intervals and Midpoint
- Class intervals could be figured by;
$18000 – = $3000, example of the first category.
Class Midpoint could be figured by
($ ) = $16500 2
* $16500 is the typical of selling price of the cars in that class. 2 2 2 2 3 2

12. Constructing Frequency Distribution
Relative Frequency Distribution
To show the fraction of total number of observations in each class.
Selling price Relative
($thousands) Frequency Frequency
$ %
$ %
$ %
$ %
$ %
$ %
$ %
Total %
Found by
8 = 10% 80 2 2 2 3 2 2

13. Constructing Frequency Distribution
Class Exercises
Page 31 2 2 2 2 3 2

14. Graphic Presentation of Frequency distribution
There are three types of charts;
1- Histogram chart
2- Frequency polygon chart
3- Cumulative frequency polygon
4- Other charts; line graphs, Bar chart, Pie chart. 2 2 2 2 3 2

15. 1- Histogram chart
A graph in which classes are marked on the horizontal axis (x) and the class frequencies on the vertical axis (y). Example , figure 1
Selling price Frequency $ $ $ $ $ $ $
Total 2 2 2 2 3 2

16. Histogram chart Number of vehicles Figure 1 40 30 23 20 18 17 8 8 10 415 18 21 24 27 30 33 36
Selling price in $000 2 2 2 2 3 2

17. 2- Frequency polygon chart
Another way to allow us to get quick picture of the main characteristics of the data ( highs, lows, points of concentration, etc)
Class midpoint in X axis and the class frequency in y axis. Figure 2, Figure 3 2 2 2 2 3 2

18. Frequency polygon
Figure 2 2 2 2 2 3 2

19. Frequency polygon
Figure 3 2 2 2 2 3 2

20. 3- Cumulative frequency polygon
Sometimes is needed to answer such questions like 50% of vehicles were sold less of what amount? ,,,,etc.
Selling price Frequency Cumulative
__________ _________ Frequency $ $ $ $ $ $ $
Total 2 2 2 2 3 2

21. Cumulative frequency polygon
Number of
Vehicles
sold
100 75 50
50% of vehicles
Sold less than $22,000 25
Selling price $000

22. 4- Other charts; line graphs, Bar chart, Pie chart.
Line charts ; show the change or trend in variable. used for stocks
Bar charts; compare ordinal scale
Pie charts; useful with nominal level data 2 2 2 2 3 2

23. Line chart 2 2 2 2 3 2

24. Bar Chart Example; Earnings of 1-Diploma High school $ 22, Bachelors $ 40, Masters $73,165 2 2 2 2 3 2

25. Pie Chart 21%% Other 26% Newspapers Golf news 29% Al khaleej news 24%
Ittihad news

26. Graphic Presentation of Frequency distribution
Class Exercises
Page 46 2 2 2 2 3 2