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Published byAlaina Doyle Modified over 8 years ago

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5 Number Summary Box Plots

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The five-number summary is the collection of The smallest value The first quartile (Q 1 or P 25 ) The median (M or Q 2 or P 50 ) The third quartile (Q 3 or P 75 ) The largest value These five numbers give a concise description of the distribution of a variable

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● The median Information about the center of the data Resistant ● The first quartile and the third quartile Information about the spread of the data Resistant ● The smallest value and the largest value Information about the tails of the data Not resistant

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● Compute the five-number summary for 1, 3, 4, 7, 8, 15, 16, 19, 23, 24, 27, 31, 33, 54 ● Calculator ● Calculations The minimum = Q 1 = M = Q 2 = Q 3 = The maximum = 54

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The five-number summary can be illustrated using a graph called the boxplot An example of a (basic) boxplot is The middle box shows Q 1, Q 2, and Q 3 The horizontal lines (sometimes called “whiskers”) show the minimum and maximum

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● To draw a (basic) boxplot: Calculate the five-number summary Draw a horizontal line that will cover all the data from the minimum to the maximum Draw a box with the left edge at Q 1 and the right edge at Q 3 Draw a line inside the box at M = Q 2 Draw a horizontal line from the Q 1 edge of the box to the minimum and one from the Q 3 edge of the box to the maximum

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Use the following times from a 5K race to make a boxplot. 19.25, 23.25, 23.32, 25.55, 25.33, 26.28, 28.58, 29.12, 30.18, 30.35

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Using the previous data, make a boxplot using a calculator.

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An example of a more sophisticated boxplot is The middle box shows Q 1, Q 2, and Q 3 The horizontal lines (sometimes called “whiskers”) show the minimum and maximum The asterisk on the right shows an outlier (determined by using the upper fence)

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Using the previous data, make an outlier boxplot using a calculator.

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● We can compare two distributions by examining their boxplots ● We draw the boxplots on the same horizontal scale We can visually compare the centers We can visually compare the spreads We can visually compare the extremes

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5-number summary Minimum, first quartile, median, third quartile maximum Resistant measures of center (median) and spread (interquartile range) Boxplots Visual representation of the 5-number summary Related to the shape of the distribution Can be used to compare multiple distributions

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