Unit 2Sections 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.

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

Section 2.1

Frequency Distribution – the organization of raw data in table form, using classes and frequency.

Class – a quantitative or qualitativecategory.

Sometimes referred to as an interval.

Frequency (f) – the number of data values that occur in a specific class.

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.

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.

Section 2.1

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

1 2 6 7 12 13 2 6 9 5 18 7 3 15 15 4 17 1 14 5 4 16 4 5 8 6 5 18 5

2 9 11 12 1 9 2 10 11 4

10 9 18 8 8 4 14 7 3 2

6

Section 2.1

Frequency Distribution

Class Limits(in Miles)

Tally Frequency

1 – 3

4 – 6

7 – 9

10 – 12

13 – 15

16 – 18

Section 2.1

Frequency Distribution

Class Limits(in Miles)

Tally Frequency

1 – 3 |||||||||| 10

4 – 6 |||||||||||||| 14

7 – 9 |||||||||| 10

10 – 12 |||||| 6

13 – 15 ||||| 5

16 – 18 ||||| 5

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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.

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 OO O B AB BB B O A O

A O O O ABAB A O B A

Construct a frequency distribution for this data.

Section 2.1

Blood Type of Army MembersClass Tally Frequency Percent

A

B

AB

O

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Blood Type of Army MembersClass Tally Frequency Percent

A ||||| 5 20%

B ||||||| 7 28%

AB |||| 4 16%

O ||||||||| 9 36%

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 – 15.5. (0.5 is added and subtracted from the limits)

A class from 5.5 – 8.5 would have a class boundary of 5.45 – 8.55. (0.05 is added and subtracted from the limits)

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.

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.

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112 100 127 120 134 118 105 110 109 112

110 118 117 116 118 122 114 114 105 109

107 112 114 115 118 117 118 122 106 110

116 108 110 121 113 120 119 111 104 111

120 113 120 117 105 110 118 112 114 114

Class Limit

Class Boundary

Frequency

Midpoint RelativeFrequenc

y

Cumulative

Frequency

Section 2.1

Class Limit

Class Boundary

Frequency

Midpoint Relative Frequenc

y

Cumulative

Frequency

100-104 99.5-104.5 2 102 0.04 2

105-109 104.5-109.5

8 107 0.16 10

110-114 109.5-114.5

18 112 0.36 28

115-119 114.5-119.5

13 117 0.26 41

120-124 119.5-124.5

7 122 0.14 48

125-129 124.5-129.5

1 127 0.02 49

130-134 129.5-134.5

1 132 0.02 50

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.

Section 2.1

Pg. 49 ( 11 -16, 29, 30)

Read and take notes on Section 2.1 (pgs. 44 - 48)

Homework