Download Measures of Central Tendency

Measures of Central
Tendency
CJ 526 Statistical Analysis in
Criminal Justice
Introduction
Central Tendency
 Single number that represents the
entire set of data (example: the
average score)

Alternate Names

Also known as _____ value
Average
 Typical
 Usual
 Representative
 Normal
 Expected

Three Measures of Central
Tendency
Mode
 Median
 Mean

The Mode
Score or qualitative category that
occurs with the greatest frequency
 Always used with nominal data, we
find the most frequently occurring
category

Mode
Example of modal category:
 Sample of 25 married, 30 single, 22
divorced
 Married is the modal category


Determined by inspection, not by
computation, counting up the
number of times a value occurs
Example of Finding the
Mode
X: 8, 6, 7, 9, 10, 6
 Mode = 6
 Y: 1, 8, 12, 3, 8, 5, 6
 Mode = 8
 Can have more than one mode
 1, 2, 2, 8, 10, 5, 5, 6
 Mode = 2 and 5

Example
Subject #
1
2
3
4
5
Mode = ?
Test Score
82
90
84
83
95
The Median
The point in a distribution that
divides it into two equal halves
 Symbolized by Md

Finding the Median
1.
2.
Arrange the scores in ascending or
descending numerical order
If there is an odd number of
scores, the Md is the middle score
Finding the Median -continued
3. If there is an even number of
scores, the median corresponds to
a value halfway between the two
middle scores
Example of Finding the
Median
X: 6, 6, 7, 8, 9, 10, 11
 Median = 8
 Y: 1, 3, 5, 6, 8, 12
 Median = 5.5

The Mean
The sum of the scores divided by the
number of scores
 The arithmetic average

Formula for finding the
Mean

Symbolized by M or “X-bar”
X

M
N
Characteristics of the Mean

The mean may not necessarily be an
actual score in a distribution
Deviation Score
Measure of how far away a given
score is from the mean
x = X - M

Example of Finding the
Mean
X: 8, 6, 7, 11, 3
 Sum = 35
N = 5
M = 7

Selecting a Measure of
Central Tendency




Choice depends on
Measurement level of data
If the data is nominal, the mode
must be used
The mode can also be used for
other levels of measurement
Shape of the Distribution
Symmetrical – Mean
 Not symmetrical—the median will be
better
 Any time there are extreme scores
the median will be better

Example
Median income: if someone loses
their job, an income of 0—this would
pull the average down
 Median housing values: an
unusually nice house or poor house
would affect the average
 Better to use the median

Central Tendency and the
Shape of a Distribution

Symmetrical

Unimodal: Mo = Md = M