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Frequency Distribution

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Title: Frequency Distribution

1
WEEK 2

Frequency Distribution
Dr. Wajed Hatamleh

2
Learning Objectives

Recognize the difference between grouped and
ungrouped data
Construct a frequency distribution
Construct a histogram

3
Overview

Descriptive Statistics
summarize or describe the important
characteristics of a known set of population
data
Inferential Statistics
use sample data to make inferences (or
generalizations) about a population

4
Important Characteristics of Data

1. Center A representative or average value
that indicates where the middle of the data set
is located
2. Variation A measure of the amount that the
values vary among themselves
3. Distribution The nature or shape of the
distribution of data (such as bell-shaped,
uniform, or skewed)
4. Outliers Sample values that lie very far
away from the vast majority of other sample
values
5. Time Changing characteristics of the data
over time

5
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

6
WHAT THE HECK ARE ALL THOSE NUMBERS??? Example of
Ungrouped Data
52 59 32 61 74 48
66 46 70 61 53 40
? ? ? ? ? ? ?
7
Frequency Distributions
HELP!!

Thats what a frequency distribution is forto
help impose order on the data
A frequency distribution is a systematic
arrangement of data values, with a count of how
many times each value occurred in a dataset

8
Key Concept

When working with large data sets, it is often
helpful to organize and summarize data by
constructing a table called a frequency
distribution.

9
Definition

Frequency Distribution (or Frequency Table)
lists data values (either individually or by
groups of intervals), along with their
corresponding frequencies or counts

10
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

11
Example of Ungrouped Data
Ages of a Sample of Nurses Managers from KFH,
KSA
12
Frequency Distribution of Nursing Managers Ages
at KFH

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

13
Data Range
Smallest
Largest
14
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

15
Class Midpoint
16
Relative Frequency

Relative
Class Interval Frequency Frequency
20-under 30 6 .12
30-under 40 18 .36
40-under 50 11 .22
50-under 60 11 .22
60-under 70 3 .06
70-under 80 1 .02
Total 50 1.00

17
Cumulative Frequency

Cumulative
Class Interval Frequency Frequency
20-under 30 6 6
30-under 40 18 24
40-under 50 11 35
50-under 60 11 46
60-under 70 3 49
70-under 80 1 50
Total 50

18
Class Midpoints, Relative Frequencies, and
Cumulative Frequencies

Relative Cumulative
Class Interval Frequency Midpoint Frequency Freque
ncy
20-under 30 6 25 .12 6
30-under 40 18 35 .36 24
40-under 50 11 45 .22 35
50-under 60 11 55 .22 46
60-under 70 3 65 .06 49
70-under 80 1 75 .02 50
Total 50 1.00

19
Cumulative Relative Frequencies

Cumulative
Relative Cumulative Relative
Class Interval Frequency Frequency Frequency Frequ
ency
20-under 30 6 .12 6 .12
30-under 40 18 .36 24 .48
40-under 50 11 .22 35 .70
50-under 60 11 .22 46 .92
60-under 70 3 .06 49 .98
70-under 80 1 .02 50 1.00
Total 50 1.00

Frequency Distributions

Another example
21
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22
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23
Lower Class Limits

are the smallest numbers that can actually
belong to different classes

24
Lower Class Limits

are the smallest numbers that can actually
belong to different classes

25
Upper Class Limits

are the largest numbers that can actually
belong to different classes

26
Class Boundaries

are the numbers used to separate classes, but
without the gaps created by class limits

27
Class Boundaries

number separating classes

28
Class Boundaries

number separating classes

29
Class Midpoints

midpoints of the classes

Class midpoints can be found by adding the lower
class limit to the upper class limit and dividing
the sum by two.
30
Class Midpoints

midpoints of the classes

49.5 149.5 249.5 349.5 449.5
31
Class Width

is the difference between two consecutive
lower class limits or two consecutive lower class
boundaries

32
Reasons for Constructing Frequency Distributions

1. Large data sets can be summarized.
2. Can gain some insight into the nature of
data.
3. Have a basis for constructing graphs.

33
Constructing A Frequency Table

1. Decide on the number of classes (should be
between 5 and 20) .
2. Calculate (round up).

(highest value) (lowest value)
class width ?
number of classes
3. Starting point Begin by choosing a lower
limit of the first class. 4. Using the lower
limit of the first class and class width, proceed
to list the lower class limits. 5. List the
lower class limits in a vertical column and
proceed to enter the upper class limits. 6. Go
through the data set putting a tally in the
appropriate class for each data value.
34
Relative Frequency Distribution
35
Relative Frequency Distribution
11/40 28 12/40 40 etc.
Total Frequency 40
36
Cumulative Frequency Distribution
Cumulative Frequencies
37
Frequency Tables
38
Recap