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Chapter 3

Sociology 2205A/B Chapter Notes - Chapter 3: Interval Ratio, Quartile, Central Tendency


Department
Sociology
Course Code
SOC 2205A/B
Professor
William Marshall
Chapter
3

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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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