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Chapter 3

This

**preview**shows half of the first page. to view the full**2 pages of the document.**1. Chapter 3: Measures of Central Tendency and

Dispersion

3.2: Nominal-level Measures

Mode: The value that occurs most frequently

oQuick and easy measurement of central tendency

oGreat for working with nominal level variables

oThere are some limitations

There sometimes isn't a mode

With ordinal and interval ratio data the modal score may not be central to the

distribution as a whole

Variation Ratio: to conveniently measure dispersion of a variable we can use a statistic based on

the mode

oThe variation ratio shows us that dispersion can be quantified and measured in even

nominal-level variables

oThe larger the variation ratio, the more dispersed the data are for that variable

o

oWhere fm= the number of cases in the mode

on = the total number of cases

3.3: Ordinal-Level Measures

Median: the exact center of a distribution of scores `

oHalf of the cases have scores higher and half lower

oMust be placed in order from highest to lowest before calculating

oWhen the number of cases is odd, the value of the median is unambiguous because

there will always be a middle case

oWith an even number of cases there will be two medians so the number exactly half way

in-between both numbers is the median

Range and Interquartile Range

oRange: difference or interval between the highest score and lowest score in a

distribution

Provides a quick and general notion of variability for variables measure at either

the ordinal or interval-ratio level

Since it is based on only the two most extreme scores in a distribution the range

will be misleading if one of these scores is exceptionally high or low

These are called outliers

oInterquartile Range: the distance from the third quartile to the first quartile of

distribution scores

Q1 is the point below which 25% of the cases fall and above which 75% of the

cases fall

Q3 is the point below which 75% of the cases fall and above which 25% of the

cases fall

Not influenced by outliers because it only uses the middle 50%

To find the quartiles:

Find the median for the ordered data set

Divide the data so there are an equal number of cases above and below

the median

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