January 16, 2014
Poli Sci 3N06
Political Science 3N06 Semester II 2014 Lecture 3b Measures of dispersion
Measures of central tendency like the mean, median and mode only tell us part of
the descriptive story
- What other things do we have to think about besides the measures of central
tendency
o How are the grades dispersed?
o The average is important but it’s not enough
o Descriptive statistics - Want to get a sense of what is going on in this
case
o Information on spread is equally as important on central tendency
Variation Ratio - Based upon the Mode
• The more cases you have in the mode
• The less variation you have in your distribution
• If every single case is one, there is no distribution / spread
• If cases begin to spread out to other cases,
• If it’s a perfectly even distribution there is no mode.
• Low variation = when all cases in one
• High variation = when all spread out
- In fact, if we describe our variables using only the central tendency
o Our lone statistic may mislead rather than inform us
- The central tendency tells us what is typical in the distribution
- What is equally important to describing a distribution is what is different in
the distribution
- The variety of scores
- There are a number of different statistics that we can use to describe the
variety, or variation, or spread, or dispersion in a distribution
- The appropriate measure depends upon the level of measurement of the
variable (amongst other considerations)
Variation ratio
- One of the few measures of dispersion that we can use for nominal-level
variables
- It can also be used for Ordinal level variables
1 January 16, 2014
Poli Sci 3N06
Range
- Can be used for ordinal or interval-ratio level variables
- Range (R ) = High Score – Low Score
- It gives a quick and easy indication of variety within the distribution
- But it is also a limited indicator
- It is based on only two scores
- So it doesn’t provide a good picture of the variety between those two scores
- It is also affected by extreme scores
Calculating the range
- 18,22,26,34,42,51,88
- 88-18=70
- How many of the scores did the data set did the range incorporate?
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Poli Sci 3N06
o How much variety is there between in the middle
o Variation within the scores is a problem
o It only takes the bottom and top (extreme scores) might not be
representative of all values in the data set!
How long to doctor?
- 1,1.5,1.5,2,2.5,3,3,3.5,67
- Range

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