1. Methods for Describing Quantitative Data
Histograms
Frequency Distribution
Methods for Describing Quantitative Data

2. 2-2 Frequency Distributions
A frequency distribution is the organizing of raw data in table form, using classes and frequencies.
The following slide shows an example of a frequency distribution.

3. 2-2 Blood Type Frequency Distribution - Example

4. 2-2 Ungrouped Frequency Distributions
2-9
Ungrouped frequency distributions - can be used for data that can be enumerated and when the range of values in the data set is not large.
Examples - number of miles your instructors have to travel from home to campus, number of girls in a 4-child family etc.

5. 2-2 Grouped Frequency Distributions
Grouped frequency distributions - can be used when the range of values in the data set is very large. The data must be grouped into classes that are more than one unit in width.
Examples - the life of boat batteries in hours.

6. 2-2 Lifetimes of Boat Batteries - Example
Class
Class
Frequency
Cumulative
limits
Boundaries
frequency 4 4 14 18 7 25

7. 2-2 Terms Associated with a Grouped Frequency Distribution
Class limits represent the smallest and largest data values that can be included in a class.
In the lifetimes of boat batteries example, the values 24 and 30 of the first class are the class limits.
The lower class limit is 24 and the upper class limit is 30.

8. 2-2 Terms Associated with a Grouped Frequency Distribution
2-14
The class boundaries are used to separate the classes so that there are no gaps in the frequency distribution.

9. 2-2 Terms Associated with a Grouped Frequency Distribution
The class width for a class in a frequency distribution is found by subtracting the lower (or upper) class limit of one class minus the lower (or upper) class limit of the previous class.

10. There should be between 5 and 20 classes.
2-2 Guidelines for Constructing a Frequency Distribution
There should be between 5 and 20 classes.
The class width should be an odd number.
The classes must be mutually exclusive.

11. The classes must be continuous. The classes must be exhaustive.
2-2 Guidelines for Constructing a Frequency Distribution
The classes must be continuous.
The classes must be exhaustive.
The class must be equal in width.

12. Find the upper class limits. Find the boundaries.
2-2 Procedure for Constructing a Grouped Frequency Distribution
Select a starting point (usually the lowest value); add the width to get the lower limits.
Find the upper class limits.
Find the boundaries.
Tally the data, find the frequencies and find the cumulative frequency.

13. 2-2 Grouped Frequency Distribution - Example
In a survey of 20 patients who smoked, the following data were obtained. Each value represents the number of cigarettes the patient smoked per day. Construct a frequency distribution using six classes. (The data is given on the next slide.)

14. 2-2 Grouped Frequency Distribution - Example

15. 2-22 Step 1: Find the highest and lowest values: H = 22 and L = 5.
2-2 Grouped Frequency Distribution - Example
2-22
Step 1: Find the highest and lowest values: H = 22 and L = 5.
Step 2: Find the range: R = H – L = 22 – 5 = 17.
Step 3: Select the number of classes desired. In this case it is equal to 6.

16. 2-2 Grouped Frequency Distribution - Example
Step 4: Find the class width by dividing the range by the number of classes. Width = 17/6 = This value is rounded up to 3.

17. 2-2 Grouped Frequency Distribution - Example
Step 5: Select a starting point for the lowest class limit. For convenience, this value is chosen to be 5, the smallest data value. The lower class limits will be 5, 8, 11, 14, 17 and 20.

19. Table 1. EPA Mileage Rating on 100 Cars*
36.3
41.0
36.9
37.1
44.9
36.8
30.0
37.2
42.1
36.7
32.7
37.3
41.2
36.6
32.9
36.5
33.2
37.4
37.5
33.6
40.5
37.6
33.9
40.2
36.4
37.7
40.0
34.2
36.2
37.9
36.0
35.9
38.2
38.3
35.7
35.6
35.1
38.5
39.0
35.5
34.8
38.6
39.4
35.3
34.4
38.8
39.7
32.5
36.1
38.4
39.3
31.8
33.1
37.0
38.7
35.8
40.7
37.8
34.5
40.3
40.1
38.0
35.2
39.5
39.9
33.8
39.8
34.0
35.0
38.1

20. Mean SAT I Math Scores by State (2003) Data Source: The College Board, New York, NY
515
501
491
518
543
576
578
613
514
502
504
519
510
549
562
588
522
498
516
540
552
559
496
525
591
594
474
512
527
517
560
582
554
521
500
541
597
506
532
553
596
583
551

21. Measurement Class (BIN)
Measurement Classes, Frequencies, and Relative Frequencies for the SAT Math Scores
Measurement Class (BIN)
Frequency
Relative Frequency
 500 5
.098
500 – 510 9
.176
510 – 520 8
.157
520 – 530 4
.078
530 – 540 3
.059
540 – 550
550 – 560
560 – 570 1
.020
570 – 580 2
.039
580 – 590
590 – 600
Greater than 600
Totals 51
1.00

22. Assignment

23. 2-3 Visualizing Data
The three most commonly used graphs in research are:
The histogram.
The frequency polygon.
The cumulative frequency graph, or ogive (pronounced o-jive).

24. Histogram Example (SAT Math Scores)

25. Histograms
Histograms condense the data by grouping similar data values into the same class (bin) in the graph.
Summarize Data
Sort
Min /Max
Range (Max – Min)
Mean (Average values)
Group
Plot

28. Frequency Versus Relative Frequency

29. 2-2 Number of Miles Traveled - Example

30. 2-2 Lifetimes of Boat Batteries - Example
Class
Class
Frequency
Cumulative
limits
Boundaries
frequency 4 4 14 18 7 25

31. 2-3 Visualizing Data
A frequency polygon is a graph that displays the data by using lines that connect points plotted for frequencies at the midpoint of classes. The frequencies represent the heights of the midpoints.

32. Example of a Frequency Polygon6 5 y c n 4 e u q 3 e r F 2 1 2 5 8 1 1 1 4 1 7 2 2 3 2 6 N u m b e r o f C i g a r e t t e s S m o k e d p e r D a y

33. 2-3 Visualizing Data
A cumulative frequency graph or ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution.

34. Example of an Ogive
Ogive

35. 2-3 Other Types of Graphs 2-41
Pie graph - A pie graph is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.

36. 2-3 Other Types of Graphs - Pie Graph
Robbery (29, 12.1%)
Pie Chart of the Number of Crimes Investigated by Law Enforcement Officers In U.S. National Parks During 1995
Rape (34, 14.2%)
Homicide (13, 5.4%)
Assaults (164, 68.3%)

37. Tabulation of data Stub Headings Sub head Sub Head
Table Number and Title
( Head or Prefatory Note )
Stub Headings
Caption
Sub head Sub Head
Column Head Column Head
Total (rows)
Stub Entries
Total (Columns)
Body or Field
Foot Note
Source Note