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PSY201H1 (45)
Chapter 3

Chapter 3

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University of Toronto St. George
Gillian Rowe

Chapter 3 Central Tendency 31 OverviewCentral tendencystatistical measure to determine a single score that defines the center of a distribution The goal of central tendency is to find the single score that is most typical or most representative of the entire group average scorealso useful for making comparisons between groups of individuals or between sets of figures Able to describe a large set of data with a single representative number The mean median and mode were created to measure central tendency 32 The MeanMeanis the sum of the scores divided by the number of scores for a distributionalso known as the arithmetic average the mean for a population is identified byand the mean for a sample is identified by M or X with a bar on top of the XFormula for the population mean XNFormula for the sample mean MXn Alternative Definitions for the MeanThink of the mean as the amount each individual would get if the total were divided equally among all individuals in the distribution example 32Think of the mean as a balance point for a distribution example 33if you positioned a seesaw at a point equal to the mean then it will be balanced and will rest levelThe Weighted MeanIts often necessary to combine two sets of scores and then find the overall mean for the combined groupto calculate the overall mean we need two values 1 The overall sum of the scores for the combined group X and 2 The total number of scores in the combined group nOverall meanMXXnn If the samples are not the same size one makes a larger contribution to the total group and therefore carries more weight in determining the overall mean and so we call it the weighted mean weighted mean is not halfway between the original two sample meansComputing the Mean from a Frequency Distribution TableCalculation of the mean is usually easier if you first remove the individual scores from the table must take into account the scores in the X column as well as their frequencies to get the overall sum of scoresTo find the total number of scores remember n f
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