1. Unit 2
Sections 2.1

2. 2.1: Frequency Distributions and Their Graphs
Section 2.1
2.1: Frequency Distributions and Their Graphs
The most convenient way of organizing data is by using a frequency table.
The most useful method of presenting data is by using charts and graphs.

3. What we will be able to do throughout this chapter…
Section 2.1
What we will be able to do throughout this chapter…
Organize data in to frequency tables.
Present data in charts and graphs.
Graphs include: histograms, frequency polygons, pie graphs, stem and leaf plots

4. Section 2.1
Frequency Distribution – the organization of raw data in table form, using classes and frequency.
Class – a quantitative or qualitative category.
Sometimes referred to as an interval.
Frequency (f) – the number of data values that occur in a specific class.

5. Section 2.1
Range – difference between the maximum data entry and the minimum data entry.
Lower class limit – smallest data value that can be included in the class.
Upper class limit – largest data value that can be included in the class.
Class width – found by subtracting the lower class limit from one class with the lower class limit of the next class.

6. Steps for Constructing a Frequency Distribution
Section 2.1
Steps for Constructing a Frequency Distribution
Decide on the number of classes needed. The number of classes should be between 5 and 20 if it is not given.
Find the class width.
Class with is the range divided by the number of classes. ALWAYS ROUND UP IF THERE IS A DECIMAL.
Find the class limits.
Make a tally mark to represent each data entry represented.
Count the tally marks to determine the frequency.

7. Section 2.1
Given the following data, create a frequency distribution using 7 classes:

8. Frequency Distribution
Section 2.1
Frequency Distribution
Class Limits
(in Miles)
Tally
Frequency
1 – 3
4 – 6
7 – 9
10 – 12
13 – 15
16 – 18

9. Frequency Distribution
Section 2.1
Frequency Distribution
Class Limits
(in Miles)
Tally
Frequency
1 – 3
|||||||||| 10
4 – 6
|||||||||||||| 14
7 – 9
10 – 12
|||||| 6
13 – 15
||||| 5
16 – 18

10. Section 2.1
The categorical frequency distribution is used for data that can be placed in specific categories (i.e. nominal or ordinal level data).
For example: grades on a test, political party, medals at the Olympics.

11. Construct a frequency distribution for this data.
Section 2.1
Activity
Twenty-five army inductees were given a blood test to determine blood type. The data set is:
A B B AB O
O O B AB B
B B O A O
A O O O AB
AB A O B A
Construct a frequency distribution for this data.

12. Blood Type of Army Members
Section 2.1
Blood Type of Army Members
Class
Tally
Frequency
Percent A B AB O

13. Blood Type of Army Members
Section 2.1
Blood Type of Army Members
Class
Tally
Frequency
Percent A
||||| 5
20% B
||||||| 7
28% AB
|||| 4
16% O
||||||||| 9
36%

14. Section 2.1
Class boundaries – numbers used to separate the classes so that there are no gaps in the frequency distribution.
For example:
A class from 10 – 15 would have a class boundary of 9.5 – (0.5 is added and subtracted from the limits)
A class from 5.5 – 8.5 would have a class boundary of 5.45 – (0.05 is added and subtracted from the limits)

15. Section 2.1
Midpoint – Sum of the lower and upper class limits, divided by two.
Relative frequency – the portion (or percentage) of the total data that falls into that class.
Class frequency divided by sample size.
Cumulative frequency – sum of the frequencies of that class and all previous classes.

16. Section 2.1
Activity
This data represents the record high temperature in Fahrenheit degrees for each of the 50 states. Construct a frequency distribution for the data using 7 classes.
112
100
127
120
134
118
105
110
109
117
116
122
114
107
115
106
108
121
113
119
111
104

17. Section 2.1 Class Limit Class Boundary Frequency Midpoint Relative
Cumulative Frequency

18. Section 2.1
Class
Limit
Class Boundary
Frequency
Midpoint
Relative
Cumulative Frequency 2
102
0.04 8
107
0.16 10 18
112
0.36 28 13
117
0.26 41 7
122
0.14 48 1
127
0.02 49
132 50

19. Reasons to Use a Frequency Distribution
Section 2.1
Reasons to Use a Frequency Distribution
To organize data in a meaningful, intelligible way.
To enable the reader to determine the nature or shape of the distribution.
To facilitate computational procedures for measures of average and spread.
To enable the researcher to draw charts and graphs for the presentation of data
To enable the reader to make comparisons among different data sets.

20. Homework
Pg. 49 ( , 29, 30)
Read and take notes on Section 2.1 (pgs )