Measures of Variability Percentile Rank

Comparison of averages is not enough. Consider a class with the following marks 80%, 80%, 80%, 90%, 20%, 70%, and 65% –The mean of the class is a 69% »A person with 70% could claim to be “above average”.

Percentile Rank Percentage of scores less than or equal to a particular score Our example –7 scores all together Only 2 of them are lower than 70% –The student was in the bottom half of the class!

Percentile Rank Where –B = number of scores below a given score –E = number of scores equal to the given score E=1 if no equal scores –n = number of scores Percentile Rank is always rounded up.

Our Example B = 2 –2 scores < 70% E = 1 –1 score = 70% n = 7 –7 scores total PR = 36 –P 36 –36 th percentile –Scored as well as or better than 36% of the class.

Special Percentiles Median –50 th Percentile –P 50 Upper quartile –Median of upper half of data –75 th Percentile –P 75 Lower quartile –Median of lower half of data –25 th Percentile –P 25

Example Wendy is 1.7m tall. She is taller than 65 of the students in her grade and no one is the same height as she is. There are 139 students in her grade. –What percentage of students are taller than Wendy?

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