Download Measures of Central Tendency

Measures of Central
Tendency
CJ 526 Statistical Analysis in
Criminal Justice
Introduction

Central Tendency
Characteristics of a Measure
of Central Tendency
1.
Single number that represents the
entire set of data (average)
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

The Median

The point in a distribution that
divides it into two equal halves

Symbolized by Md
Finding the Median
1.
Arrange the scores in ascending or
descending numerical order
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
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
Nature of the Variable

Nominal -- Mode
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

Intended Use of Statistic

Descriptive -- Mode, Median, or
Mean
Central Tendency and the
Shape of a Distribution

Symmetrical

Unimodal: Mo = Md = M