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is a statistical 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 respresentative of the entire group
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the sum of the score divided by the number of the scores.
Most commonly used
M = (∑x)/n |
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the score that divides a distribution exactly in half. Exactly 50% of the individuals in a distribution have scores at or below the median. The median is equivalent to the 50th percentile
# of places = (n+1)/2
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| In a frequency distribution, the mode is the score or category that has the greatest frequency. |
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| a distribution with two modes |
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| a distribution with more than two modes |
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represents a set of scores or numbers that is not equal on both sides. This results from a few scores in a data set falling farther to one end or the other.
Two Types: Negative and Positive |
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| Negative Skew Distribution |
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| Positive Skew Distribution |
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| Symnmetrical Distribution |
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| provides a quantitiative measure of the degree to which scores in a distribution are spread out or clustered together. |
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the difference between the upper real limit of the largest (maximum) X value and the lower real limit of the smallest (minimum) X value.
simplest measure of variability |
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| Interquartile Range (IQR) |
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the range covered by the middle 50% of the distribution
count in (n + 1)/4 places
IQR = Q3 - Q1
Measurement scale: Ordinal; Median |
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| half of the interquartile range |
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S2 = (∑x2- (∑x)2/n) n - 1
the mean of the squared deviation scores
index describing how an individual score (x) varies from its mean |
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measures how far off all of the individuals in the distribution are from a standard, where that standard is the mean of the distribution.
Standard Deviation - √variance
SD = √s2 |
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| the sum of the squared deviation scores |
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| for a sample of n scores, the Degrees of Freedom (df) for the sample variance are defined as df = n - 1. The Degrees of Freedom (df) determine the number of scores that are independent and are free to vary. |
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| a sample is unbiased if the average value of the sample statistic, obtained over many different samples, is equal to the population parameter. |
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| if the average value for a sample statistic consistently underestimates or overestimates the corresponding population parameter, then the statistic is biased. |
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| Factors that Affect Variability |
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- Extreme Scores
- Sample Size
- Stability Size
- Stability under sampling
- Open-ended distributions
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A z-score specifies the precise location of each X value within a distribution. The sign of the z-score (+ or -) signifies whether the score is above the mean or below the mean. The numerical value of the z-score specifies the distance from the mean by counting the number of standard deviations between X and m.
Z = x - M (sample mean)
SD |
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Mode and median can be used
Median preferable |
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- Mean, Median, and Mode can be used
- Mean uses every score in the distribution in its calculation
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