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Chapter 4

# L33 Psych 300 Chapter 4: Central Tendency and Variability

Department
Psychological & Brain Sci (Psychology)
Course Code
L33 Psych 300
Professor
Nestojko
Chapter
4

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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
βMean, the Arithmetic Average
βMean in Plain English - the arithmetic average of a group of scores (often just
called the average), a precise number that should be the βtypicalβ score in a
distribution
βMean in Plain Arithmetic - calculated by summing all the scores in a data set and
dividing this sum by the total number of scores
βMean Expressed by Symbolic Notation - ξM
ξ
or βX-barβ (X with a bar above)
β The numbers based on ξsξamples taken from a population are called
sξtatistics; M is a statistic. The numbers based on whole ξpξopulations are
called ξpξarameters, βUβ is a parameter. βUβ is pronounced βMewβ
βHow to calculate the mean: add up all the scores and divide by the # of scores
βMedianξ - the middle score of all the scores in a sample when the scores are arranged in
ascending order
βWith an odd number of scores, there will be an actual middle score
βWith an even number of scores, there will be no actual middle, so you have to
calculate the mean (average) of the two middle scores
βModeξ - the most common score of all the scores in a sample
βWhen 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
βUnimodalξ - when a distribution of scores has one mode
βBimodalξ - when a distribution of scores has two modes
βMultimodalξ - when a distribution of scores has more than two modes
Measures of Variability
βVariability - a numerical way of describing how much spread there is in a distribution
βNumerically - range
βComputing variance and its square root, known as standard deviation
βRangeξ - a measure of variability calculated by subtracting the lowest score (minimum)
from the highest score (maximum)
βRange = X(highest) - X(lowest)
βVarianceξ - the average of the standard deviations from the mean
βHow do we calculate the variance?
βSubtract the mean from every score
βSquare every deviation from the mean
βSum all of the squared deviations
βDivide the sum of squares by the total number in the sample (N)
βStandardξ ξDeviationξ - the square root of the average of the squared deviations from
the mean, or more simply, the square root of the variance