Section 2.1

Frequency Distributions

HAWKES LEARNING SYSTEMS

math courseware specialists

Copyright © 2008 by Hawkes Learning

Systems/Quant Systems, Inc.

All rights reserved.

Graphical Descriptions of Data

2.1 Frequency Distributions

HAWKES LEARNING SYSTEMS

math courseware specialists

• Ordered array – an ordered list of the data from largest to smallest or vice versa.

• Distribution – displays data values that occur and how often they occur. It can be a chart or a table.

• Frequency Distribution – table that divides data into groups, called classes, and shows how many data values occur in each group.

• Frequency, f – number of data values in a class.

Organizing Data:

Graphical Descriptions of Data

2.1 Frequency Distributions

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1. Decide on the number of classes• Between 5 and 20

2. Choose an appropriate class width•

3. Find the class limits• Start with the lowest value and add the class

width to get the next class limit.

4. Determine the frequency of each class• Count the number of data values in each

class.

Creating frequency tables:

Graphical Descriptions of Data

2.1 Frequency Distributions

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math courseware specialists

1. Classes boundaries• Split the difference in the gap between the upper limit of one

class and the lower limit of the next class.

2. Midpoints

•

3. Relative Frequency

•

4. Cumulative Frequency• The sum of the frequency for a given class and all previous

classes.

Other characteristics can be calculated once the basic frequency table has been constructed:

Graphical Descriptions of Data

2.1 Frequency Distributions

HAWKES LEARNING SYSTEMS

math courseware specialists

Create a frequency distribution using 5 classes:

Quiz Grades

9 3 5 4 7

8 10 8 6 7

4 5 2 7 8

10 7 9 10 1

8 6 10 9 8

Solution – First place the data in an ordered array:

Quiz Grades – Ordered Array

1 2 3 4 4

5 5 6 6 7

7 7 7 8 8

8 8 8 9 9

9 10 10 10 10

Graphical Descriptions of Data

2.1 Frequency Distributions

HAWKES LEARNING SYSTEMS

math courseware specialists

Since we have the smallest and largest values, we can find the class width.

Round 1.8 up to a sensible value, 2.

Next begin building the class limits with the smallest data value in the set.

Solution – continued:

Graphical Descriptions of Data

2.1 Frequency Distributions

HAWKES LEARNING SYSTEMS

math courseware specialists

The frequency distribution:

Quiz Grades

Class fClass

BoundariesMidpoint

Relative Frequency

Cumulative Frequency

1 – 2 2 0.5 – 2.5 1.5 2

3 – 4 3 2.5 – 4.5 3.5 5

5 – 6 4 4.5 – 6.5 5.5 9

7 – 8 9 6.5 – 8.5 7.5 18

9 – 10 7 8.5 – 10.5 9.5 25

20.08

25

30.12

25

40.16

25

90.36

25

70.28

25

Graphical Descriptions of Data

2.1 Frequency Distributions

HAWKES LEARNING SYSTEMS

math courseware specialists

Create a frequency distribution using 6 classes:

GPA’s

3.2 2.6 2.9 2.0 3.1

3.5 1.8 1.3 3.8 3.0

1.1 2.0 2.5 3.1 3.4

Solution – First place the data in an ordered array:

GPA’s – Ordered Array

1.1 1.3 1.8 2.0 2.0

2.5 2.6 2.9 3.0 3.1

3.1 3.2 3.4 3.5 3.8

Graphical Descriptions of Data

2.1 Frequency Distributions

HAWKES LEARNING SYSTEMS

math courseware specialists

Since we have the smallest and largest values, we can find the class width.

Round 0.45 up to a sensible value, 0.5.

Next begin building the class limits with the smallest data value in the set.

Solution – continued:

Graphical Descriptions of Data

2.1 Frequency Distributions

HAWKES LEARNING SYSTEMS

math courseware specialists

The frequency distribution:

Quiz Grades

Class fClass

BoundariesMidpoint

Relative Frequency

Cumulative Frequency

1.0 – 1.4 2 0.95 – 1.45 1.2 2

1.5 – 1.9 1 1.45 – 1.95 1.7 3

2.0 – 2.4 2 1.95 – 2.45 2.2 5

2.5 – 2.9 3 2.45 – 2.95 2.7 8

3.0 – 3.4 5 2.95 – 3.45 3.2 13

3.5 – 3.9 2 3.45 – 3.95 3.7 15

20.133

15

10.067

15

30.200

15

50.333

15

20.133

15

20.133

15