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 Tendency๎€ - 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
โ—Mean, the Arithmetic Average
โ—‹Mean in Plain English - the arithmetic average of a group of scores (often just
called the average), a precise number that should be the โ€œtypicalโ€ score in a
distribution
โ—‹Mean in Plain Arithmetic - calculated by summing all the scores in a data set and
dividing this sum by the total number of scores
โ—‹Mean Expressed by Symbolic Notation - ๎€M
๎€
or โ€œX-barโ€ (X with a bar above)
โ– The numbers based on ๎€s๎€amples taken from a population are called
s๎€tatistics; M is a statistic. The numbers based on whole ๎€p๎€opulations are
called ๎€p๎€arameters, โ€œUโ€ is a parameter. โ€œUโ€ is pronounced โ€œMewโ€
โ—‹How to calculate the mean: add up all the scores and divide by the # of scores
โ—Median๎€ - the middle score of all the scores in a sample when the scores are arranged in
ascending order
โ—‹With an odd number of scores, there will be an actual middle score
โ—‹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
โ—Mode๎€ - the most common score of all the scores in a sample
โ—‹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
โ—‹Unimodal๎€ - when a distribution of scores has one mode
โ—‹Bimodal๎€ - when a distribution of scores has two modes
โ—‹Multimodal๎€ - when a distribution of scores has more than two modes
Measures of Variability
โ—Variability - a numerical way of describing how much spread there is in a distribution
โ—‹Numerically - range
โ—‹Computing variance and its square root, known as standard deviation
โ—Range๎€ - a measure of variability calculated by subtracting the lowest score (minimum)
from the highest score (maximum)
โ—‹Range = X(highest) - X(lowest)
โ—Variance๎€ - the average of the standard deviations from the mean
โ—How do we calculate the variance?
โ—‹Subtract the mean from every score
โ—‹Square every deviation from the mean
โ—‹Sum all of the squared deviations
โ—‹Divide the sum of squares by the total number in the sample (N)
โ—Standard๎€ ๎€Deviation๎€ - 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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