Measures that determine the position of a single value in relation to other values in a data set. Quartiles, percentiles, and percentile rank are examples of measures of position.
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z-scores
measure the distance of a score from the mean in units of standard deviation
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positive
if the data value is larger than the mean it is a _____ z-score
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negative
if the data value is smaller than the mean it is a _____ z-score
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Percintile
breaks observation into 100 parts
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Z = (X - μ) / σ
z score formula
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-1 and 1
68%
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-2 and 2
95%
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-3 and 3
99.7%
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quartiles
Values that divide a data set into four equal parts
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first quartile
25th percentile
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second quartile
the median of the entire data set
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third quartile
the median of the upper half of the data set
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Interquartile Range (IQR)
Q3-Q1, the middle 50% of the data, resistant
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Q1-1.5(IQR)
lower fence
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Q3 + 1.5(IQR)
upper fence
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median and IQR
are better measures of center and spread for skewed distributions.
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mean and standard deviation
are better measures of center and spread for relatively symmetric distributions.
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five number summary
minimum, Q1, median, Q3, maximum
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Boxplot
A graph of the five-number summary., number line, box from lower quartile Q1 to upper quartile Q3, line at median, line to smallest and largest (not outliers)