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Lecture 2

# PS296 Week 2B (Measures of Central Tendency)

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Wilfrid Laurier University

Psychology

PS296

Max Gwynn

Winter

Description

PS296 Week 2B (Measures of Central Tendency)
• Numerical values that refer to the centre of the distribution
• A measure of central tendency provides a single value on a measurement scale that represents
the location (“average”) of a set of scores.
3 measures: Mode , Median, and Mean
Mode (Mo):
• Most frequently occurring score or scores in a set of data; the most common value
• The highest point in a frequency distribution
• May not be unique; there may be more than one mode in a distribution (multimodal)
Median (Mdn):
• score in the middle of the ranked distribution
• the score above and below which fall the same number of scores
th
• the 50 percentile
• The score corresponding to the point having 50 % of the observations below it when
observations are arranged in numerical order
• the middle value or mean of two middle values
• Data: 4, 9, 16, 5, 8, 7, 3, 4, 8, 11, 10, 8, 5
• Difficult to determine the median in an unordered data set.
• Rank the data first, from lowest to highest! 3, 4, 4, 5, 5, 7, 8, 8, 8, 9, 10, 11, 16
• Then determine the median location.
Median location:
• the location of the median in an ordered series
• with an odd number of scores, median location is
(N+1)/2
• where N equals the number of scores in the ranked distribution • with an even number of scores, median is the average of the middle two scores in the ranked
distribution
Median determination: Odd number of scores
3, 4, 4, 5, 5, 7, 8, 8, 8, 9, 10, 11, 16
• N = 13
• Median location = (N+1)/2
= (13 + 1) /2
= 14/2 = 7
th
• So the median is in the 7 location, which corresponds to the value 8
• Note that the median is NOT 7!
– 7 is the median location
Median determination: Even number of scores
23, 54, 67, 12, 19, 98 ranked: 12, 19, 23, 54, 67, 98
• N = 6
• Median location = (N+1)/2
= (6 + 1) /2
= 7/2 = 3.5
• So the median is in the 3.5 location,
rd th
• We take the average of the values in the 3 and 4 locations
• which corresponds to the values of 23 and 54
• The average of 23 and 54 is (23+54)/2

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