math 30 lecture 3 - PROBABILITY AND STATISTICS MEASURES OF...

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PROBABILITY AND STATISTICS MEASURES OF VARIABILITY/ GROUPED DATA MATH 30: PROBABILITY AND STATISTICS
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Recall: Mean is the average of all data values. Median is the midpoint of all data values when arranged from lowest to highest. Mode is the data value with the highest frequency. Skewness refers to the symmetry (or the lack of symmetry) of the distribution. MATH 30: PROBABILITY AND STATISTICS
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MATH 30: PROBABILITY AND STATISTICS In summary, Measures of location Mean Median Mode Type of data I, R I, R, O N Extreme score problem Yes No No Always measurable Yes Yes No Number of values 1 1 0, 1, 2, … In/out of the set of data In/out In/out In Characteristics All scores are taken into account Middle value Popular value I interval, R rational, O ordinal, N nominal
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MATH 30: PROBABILITY AND STATISTICS Other Measures of Location Trimmed mean A trimmed mean is computed by “trimming away” a certain percent of both the largest and smallest set of values. For example the 10% trimmed mean is found by eliminating the largest 10% and smallest 10% and computing the average of the remaining values.
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MATH 30: PROBABILITY AND STATISTICS Other Measures of Location QUANTILES are points taken at regular intervals from the cumulative distribution function of a random variable. Dividing ordered data into q essentially equal- sized data subsets is the motivation for q - quantiles.
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MATH 30: PROBABILITY AND STATISTICS Other Measures of Location The popular quartiles are as follows: Quartile One fourth m = 1,2,3 ?
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