3.3: Percentiles and Box-and-Whiskers Plots

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3.3 Percentiles and Box-and-Whiskers Plots

• Understandable Statistics 10th edition
• By Brase and Brase

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Summary Measures
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Percentiles

• For any whole number P (between 1 and 99), the
  Pth percentile of a distribution is a value such
  that P of the data fall at or below it.
• The percent falling above the Pth percentile will
  be (100 P).

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Percentiles
40 of data
60 of data
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(No Transcript)
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Quartiles

• Percentiles that divide the data into fourths.
• Q1 25th percentile
• Q2 the median
• Q3 75th percentile

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Quartiles
Q2
Q1
Q3
Highest value
Lowest value
Inter-quartile range IQR Q3 Q1
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Computing Quartiles

• Order the data from smallest to largest.
• Find the median, the second quartile.
• Find the median of the data falling below Q2.
  This is the first quartile.
• Find the median of the data falling above Q2.
  This is the third quartile.

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Find the quartiles
12 15 16 16 17 18 22 22 23 24 25 30
32 33 33 34 41 45 51
The data has been ordered. The median is 24.
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Find the quartiles
12 15 16 16 17 18 22 22 23 24 25 30
32 33 33 34 41 45 51
For the data below the median, the median is
17. 17 is the first quartile.
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Find the quartiles
12 15 16 16 17 18 22 22 23 24 25 30
32 33 33 34 41 45 51
For the data above the median, the median is
33. 33 is the third quartile.
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Find the interquartile range

• 12 15 16 16 17 18 22 22
• 23 24 25 30 32 33 33 34
• 41 45 51

IQR Q3 Q1 33 17 16
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Five-Number Summary of Data

• Lowest value
• First quartile
• Median
• Third quartile
• Highest value

Box-and-Whiskers Plot
A graphical presentation of the five-number
summary of data.
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Making a Box-and-Whisker Plot

• Draw a vertical scale including the lowest and
  highest values.
• To the right of the scale, draw a box from Q1 to
  Q3.
• Draw a solid line through the box at the median.
• Draw lines (whiskers) from Q1 to the lowest and
  from Q3 to the highest values.

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Construct a Box-and-Whisker Plot
12 15 16 16 17 18 22 22 23 24 25 30
32 33 33 34 41 45 51
Lowest 12 Q1 17 median 24 Q3 33 Highest
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Box-and-Whisker Plot
Lowest 12 Q1 17 median 24 Q3 33 Highest
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