1. Business Statistics
Chapter 2
Charts
& Graphs
by Ken Black

2. Learning Objectives
Recognize the difference between grouped and ungrouped data
Construct a frequency distribution
Construct a histogram, a frequency polygon, an ogive, a pie chart, a stem and leaf plot, a Pareto chart, and a scatter plot 2

3. Ungrouped Versus Grouped Data
Ungrouped data
have not been summarized in any way
are also called raw data
Grouped data
have been organized into a frequency distribution 7

4. Example of Ungrouped Data42 30 53 50 52 55 49 61 74 26 58 40 28 36 33 31 37 32 23 43 29 34 47 35 64 46 57 25 60 54
Ages of a Sample of
Managers from
Tata Company
in India 8

5. Frequency Distribution of Tata company Manager’s Ages
Class Interval Frequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1 9

6. Data Range Smallest Largest 42 30 53 50 52 55 49 61 74 26 58 40 28 3633 31 37 32 23 43 29 34 47 35 64 46 57 25 60 54
Smallest
Largest 10

7. Number of Classes and Class Width
The number of classes should be between 5 and 15.
Fewer than 5 classes cause excessive summarization.
More than 15 classes leave too much detail.
Class Width
Divide the range by the number of classes for an approximate class width
Round up to a convenient number 11

8. Class Midpoint 12

9. Relative Frequency Relative Class Interval Frequency Frequency
20-under
30-under
40-under
50-under
60-under
70-under
Total 13

10. Cumulative Frequency Cumulative Class Interval Frequency Frequency
20-under
30-under
40-under
50-under
60-under
70-under
Total 50 14

11. Class Midpoints, Relative Frequencies, and Cumulative Frequencies
Relative Cumulative
Class Interval Frequency Midpoint Frequency Frequency
20-under
30-under
40-under
50-under
60-under
70-under
Total 15

12. Cumulative Relative Frequencies
Relative Cumulative Relative
Class Interval Frequency Frequency Frequency Frequency
20-under
30-under
40-under
50-under
60-under
70-under
Total 16

13. Common Statistical Graphs
Histogram -- vertical bar chart of frequencies
Frequency Polygon -- line graph of frequencies
Ogive -- line graph of cumulative frequencies
Pie Chart -- proportional representation for categories of a whole
Stem and Leaf Plot
Scatter Plot 17

14. Histogram Class Interval Frequency 20-under 30 6 30-under 40 18

15. Histogram Construction
Class Interval Frequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1 19

16. Frequency Polygon Class Interval Frequency 20-under 30 6

17. Ogive Cumulative Class Interval Frequency 20-under 30 6 30-under 40 2421

18. Relative Frequency Ogive
Cumulative
Relative
Class Interval Frequency
20-under
30-under
40-under
50-under
60-under
70-under 22

19. Safety Examination Scores for Plant Trainees
Raw Data
Stem
Leaf 2 3 4 5 6 7 8 9 3 9
7 9
5 6 9 86 76 23 77 81 79 68 92 59 75 83 49 91 47 72 82 74 70 56 60 88 97 39 78 94 55 67 89 28

20. Construction of Stem and Leaf Plot
Raw Data
Stem
Leaf 2 3 4 5 6 7 8 9 3 9
7 9
5 6 9 86 76 23 77 81 79 68 92 59 75 83 49 91 47 72 82 74 70 56 60 88 97 39 78 94 55 67 89
Stem
Leaf
Stem
Leaf 29

21. Scatter Plot Registered Vehicles (1000's)
Gasoline Sales (1000's of Gallons) 5 60 15
120 9 90
140 7

22. A X company surveyed age of 53 of its middle level managers
A X company surveyed age of 53 of its middle level managers. Which has later been organised into frequency distribution as shown below. Determine the class midpoint, relative frequency & Cum. R.F for these data. Compute a histogram, frequency polygon, Ogive & Pie chart for the same. CI F
20-25 8
25-30 6
30-35 5
35-40 12
40-45 15
45-50 7

23. Thank U