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

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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

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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 -

40 -

35 -

30 -

25 -

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15 -

10 -