January 15, 2014
Political Science 3N06
Political Science 3N06 Semester II 2014 Lecture 3a: Measures of Central
- Recall our discussion of Frequency Tables – the first step before we can
analyze our data
RS HIGHEST DEGREE
Frequency Percent Valid Percent Cumulative Percent
Valid LT HIGH SCHOOL 217 14.9 14.9 14.9
HIGH SCHOOL 801 54.9 54.9 69.8
COLLEGE 100 6.8 6.9 76.6
BACHELOR 222 15.2 15.2 91.8
GRADUATE 119 8.2 8.2 100.0
Total 1459 99.9 100.0
Missing DK 1 .1
Total 1460 100.0
Measure of dispersion gives you a sense of variety.
- Information on the shape of the distribution
o Important when talking about the things such as a normal curve.
- Frequency distributions bring order and meaning to our data
- But we can summarize and condense our distribution even further
- The key is to find values that are in some way “representative of the entire
- And that brings us to today’s topic: Measures of Central Tendency
o A measure of central tendency, it’s a number that gives us a sense
of what’s at the center of the variables.
o What is most typical?
o More than one measure of central tendency.
o We need to understand MODE, MEDIAN and MEAN
- There is more than one measure of central tendency
- So we have a choice in terms of what value we treat as typical or average or
representative of a distribution
- Mode, Median, and Mean
- The key is to know which of these measures of central tendency should be
used in which circumstances
1 January 15, 2014
Political Science 3N06
- Knowing which to use is determined by:
- 1. The level of measurement of the variable in question
o ORDINAL, NOMINAL OR INTERVAL?
- 2. The shape of the distribution
o Is the data symmetrically distributed or is there a skew?
o If there is a skew not going to want to use the mean, median is more
- 3. The purpose of the research
o Different purposes call for different numbers
- The mode is the variable category that is most common in your distribution
o The score that occurs with the highest frequency
- It is the only measure of central tendency available for nominal-level
- It can also be reported for ordinal and interval-ratio level variables -
although other measures of central tendency will provide more (and
sometimes better) information
- 1,1,4,2,6,1,9 Mode (1)
- Conservative, liberal, NDP, NDP, NDP, Liberal 3 is the Frequency of the
most common category, but the Mode is NDP.
o Using the frequency to identify the Mode.
- If there’s an equal distribution there is NO MODE.
o If we are talking about nominal level variables, the mode is the only
measure of central tendency that we can report.
Cannot order a nominal level variable into Median / Mean
o Can also report the mode when talking about Ordinal and interval
Not the best indicator of central tendency
The most common score is not the CENTRAL score
It might not tell us anything about what is typical about the
It might not be representative of what is taking place inside of
the data set
The mode is not always good indicator of central tendency
Does not incorporate every value in the data set