Department

Psychological & Brain Sci (Psychology)Course Code

L33 Psych 300Professor

NestojkoChapter

4This

**preview**shows half of the first page. to view the full**1 pages of the document.**Chapter 04: Central Tendency and Variability

Central Tendencyξ - the descriptive statistic that best represents the center of the data set, the

particular value that all the other data seems to be gathering around

βMean, the Arithmetic Average

βMean in Plain English - the arithmetic average of a group of scores (often just

called the average), a precise number that should be the βtypicalβ score in a

distribution

βMean in Plain Arithmetic - calculated by summing all the scores in a data set and

dividing this sum by the total number of scores

βMean Expressed by Symbolic Notation - ξM

ξ

or βX-barβ (X with a bar above)

β The numbers based on ξsξamples taken from a population are called

sξtatistics; M is a statistic. The numbers based on whole ξpξopulations are

called ξpξarameters, βUβ is a parameter. βUβ is pronounced βMewβ

βHow to calculate the mean: add up all the scores and divide by the # of scores

βMedianξ - the middle score of all the scores in a sample when the scores are arranged in

ascending order

βWith an odd number of scores, there will be an actual middle score

βWith an even number of scores, there will be no actual middle, so you have to

calculate the mean (average) of the two middle scores

βModeξ - the most common score of all the scores in a sample

βWhen there is no specific mode, we can report the most common interval as the

mode; for example, we would say that the mode on a test is 80-89

βUnimodalξ - when a distribution of scores has one mode

βBimodalξ - when a distribution of scores has two modes

βMultimodalξ - when a distribution of scores has more than two modes

Measures of Variability

βVariability - a numerical way of describing how much spread there is in a distribution

βNumerically - range

βComputing variance and its square root, known as standard deviation

βRangeξ - a measure of variability calculated by subtracting the lowest score (minimum)

from the highest score (maximum)

βRange = X(highest) - X(lowest)

βVarianceξ - the average of the standard deviations from the mean

βHow do we calculate the variance?

βSubtract the mean from every score

βSquare every deviation from the mean

βSum all of the squared deviations

βDivide the sum of squares by the total number in the sample (N)

βStandardξ ξDeviationξ - the square root of the average of the squared deviations from

the mean, or more simply, the square root of the variance

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