Post on 05-Jan-2016
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)%.
Percentiles
40% of data
Low
est
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Hig
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lueP 40
60% of data
Quartiles
• Percentiles that divide the data into fourths
• Q1 = 25th percentile
• Q2 = the median
• Q3 = 75th percentile
Quartiles
Q1
Median = Q2
Q3
Inter-quartile range = IQR = Q3 — Q1
Low
est
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Hig
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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.
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.
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.
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.
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.
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
Five-Number Summary of Data
• Lowest value
• First quartile
• Median
• Third quartile
• Highest value
Box-and-Whisker Plot
a graphical presentation of the five-number summary of data
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.
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 = 51
Box-and-Whisker Plot
Lowest = 12
Q1 = 17
median = 24
Q3 = 33
Highest = 51
60 -
55 -
50 -
45 -
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35 -
30 -
25 -
20 -
15 -
10 -