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3.3 Measures of Relative Standing and Boxplots Percentiles and Quartiles: The 𝒌𝒕𝒉 percentile is the number 𝑃 with the property that approximately 𝑘 percent of the data is to the left of 𝑃 and the rest of the data is to the right of 𝑃 .

The Quartiles 𝑄 , 𝑄 , and 𝑄 divide the data into roughly four equal parts. 𝑄 is the ________ percentile 𝑄 is the_________percentile 𝑄 is the_________percentile

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3.3 Percentiles and Boxplots (Continued) Method for Finding Percentiles: Example 3.3.1 15,13,6,5,12,50,22,18,17,10

3.3 Percentiles and Boxplots (Continued) The interquartile range (IQR) is defined by 𝐼𝑄𝑅  𝑄  𝑄 and is the range for the middle 50% of the data. An outlier is an unusually large or small data value compared with the rest of the data values. Any data value smaller than 𝑄  1.5𝐼𝑄𝑅 or larger than 𝑄  1.5𝐼𝑄𝑅 is considered to be an outlier.

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3.3 Percentiles and Boxplots (Continued) Example 3.3.1 (Continued)

15,13,6,5,12,50,22,18,17,10

𝑄  10 𝑄  14 𝑄  18 𝐼𝑄𝑅  𝑄  𝑄 𝑄  1.5𝐼𝑄𝑅 𝑄  1.5𝐼𝑄𝑅

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3.3 Percentiles and Boxplots (Continued) Boxplots The five-number summary consists of the values min, 𝑄 , 𝑄 , 𝑄 , max

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3.3 Percentiles and Boxplots (Continued) Example 3.3.1 (Continued)

15,13,6,5,12,50,22,18,17,10

𝑄  10 𝑄  14 𝑄  18

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3.3 Percentiles and Boxplots (Continued) Modified Boxplots Let 𝑎 be the largest value that is not an outlier. Let 𝑎 be the smallest value that is not an outlier. 𝑎 and 𝑎 are called adjacent values. Example 3.3.1 (Continued) 15,13,6,5,12,50,22,18,17,10

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3.3 Percentiles and Boxplots (Continued) Example 3.3.1 (Continued)

𝑎  22 𝑎  5 𝑄  10 𝑄  14 𝑄  18

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3.3 Percentiles and Boxplots (Continued) The Effect of Age on Covid-19 Outcome

(Source: https://towardsdatascience.com/see-the-coronavirus-for-yourself-88ce06b88f5e)

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