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Review of Statistics. Mean, Median, Mode and Range. Mean – The sum of the data divided by the number of items in the data set. Median – T he middle number of the data ordered from least to greatest, or the mean of the middle two numbers. Mode – The number or numbers that occur most often.
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Mean, Median, Mode and Range • Mean – The sum of the data divided by the number of items in the data set. • Median – The middle number of the data ordered from least to greatest, or the mean of the middle two numbers. • Mode – The number or numbers that occur most often. • There can be more than one mode. • Range - The difference between the largest number in the data set and the smallest number in the data set.
Measures of Variation • Lower quartile (LQ) • The median of the lower half of the set of data. • Upper quartile (UQ) • The median of the upper half of the set of data. • Interquartile range • The range of the middle half of the data. • The difference between the upper quartile and the lower quartile. • Outlier • Avalue that is much greater or much less than the median. • Data that are more than 1.5 times the value of the interquartile range beyond the quartiles.
Practice Problem • Find the median, upper and lower quartiles, interquartile range and any outliers for the following data set: 81, 79, 88, 67, 89, 87, 85, 83, 83 Put them in order from least to greatest: 67, 79, 81, 83, 83, 85, 87, 88, 89 Upper half: 85, 87, 88, 89 Upper Quartile (87+88)÷2 = 87.5 Lower half: 67, 79, 81, 83 Lower Quartile (79+81)÷2 = 80 83 is the median Outliers 7.5(1.5) = 11.25 Lower limit 80-11.25 = 68.75 Upper limit 87.5+11.25 = 98.75 Interquartile range Upper Quartile – Lower Quartile 87.5 – 80 = 7.5 67 is an outlier because it is less than 68.75
Reading Box-and-Whisker Plots • A professor asked her students to keep track of how many websites they visit each day. This box-and-whisker plot shows the results. Find the following values: Minimum: LQ: Maximum: UQ: Range: Interquartile Range: Median: 4 5 10 8 6 3 7
Stem & Leaf Plot • Make a stem and leaf plot for the following data set: 78, 67, 54, 46, 77, 65, 53, 43, 75, 64, 52, 40, 51, 62,and 50 Stem Leaf 40 3 6 50 1 2 3 4 62 4 5 7 7 5 7 8