For Problem 8, find the first quartile, the median, and the third quartile, and draw the corresponding box-and-whisker diagram. a) 1,3,5,6,8,8,10b) 9,10,16,17,21,25,25,25c)15,16,18, 22,24,30,37,39,44d)23,31,37,39,40,42,44,48,65 shown below.Note: In a box-and-whisker diagram, the width of the box is arbitraryA bar-and-whisker diagram can be drawn vertically506asExample 5.- maximum value504++ Q,502 -Volume (mL)+ median500+< Q,498 +496 -+ minimum valueSolution:494Figure 5.7Example 5.6:Consider the following set of data:4,8, 9, 10, 11, 13, 15Find the median, the first quartile, and the thirda.quartile.Draw a box-and-whisker diagram to represent theb.data.Solution:Median = 10a.First quartile = 8Third quartile 13b. The required box-and-whisker diagram is shownbelow.Wecompa:examp.Examp46.810121416Figure 5.8without affecting the meaning of the display.274 quartile, the median, the third quartile, and the maximum value of the data.A box-and-whisker diagram (also called a boxplot) is used to displayinformation of a set of data, including the minimum value, the first10 selected bottles from filling line A that we have discussed in Section 5.1.Below is a box-and-whisker diagram for the volumes of soft drink in theMore on Box-and-WhiskerDiagramsdata has asomen home to+494502Volume (mL)Figure 5.5496498500504506rel time ofThe box contains the middle 50% of the data. The median is markedtr the vertical line segment in the box. The first quartile (Q) and the thirdortile (0,) are marked by the left edge and the right edge of the box,espectively. The line segments extending from the edges of the box to theninimum value and the maximum value are called whiskers. Each whiskereights ofcontains 25% of the data.medianmaximum valueminimum value25% of data25% of data 25% of dataFigure 5.625% of dataof constructing a box-and-whisker diagram are given below:stepsTheMATH FOGUEDraw a box that reaches from the first quartile to thethird quartile on a horizontal scale.Draw a vertical line segment across the box at themedian.Step 1.Step 2.Draw a line segment from the left edge of the box tothe minimum value.Siep 3.Draw a line segment from the right edge of the box tothe maximum value.Step 4.273

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Description: For Problem 8, find the first quartile, the median, and the third quartile, and draw the corresponding box-and-whisker diagram. a) 1,3,5,6,8,8,10b) 9,10,16,17,21,25,25,25c)15,16,18, 22,24,30,37,39,44d)23,31,37,39,40,42,44,48,65 shown below.Note: In a

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For Problem 8, find the first quartile, the median, and the third quartile, and draw the corresponding box-and-whisker diagram.

a) 1,3,5,6,8,8,10

b) 9,10,16,17,21,25,25,25

c)15,16,18, 22,24,30,37,39,44

d)23,31,37,39,40,42,44,48,65

shown below.
Note: In a box-and-whisker diagram, the width of the box is arbitrary
A bar-and-whisker diagram can be drawn vertically
506
as
Example 5.
- maximum value
504+
+ Q,
502 -
Volume (mL)
+ median
500+
< Q,
498 +
496 -
+ minimum value
Solution:
494
Figure 5.7
Example 5.6:
Consider the following set of data:
4,8, 9, 10, 11, 13, 15
Find the median, the first quartile, and the third
a.
quartile.
Draw a box-and-whisker diagram to represent the
b.
data.
Solution:
Median = 10
a.
First quartile = 8
Third quartile 13
b. The required box-and-whisker diagram is shown
below.
We
compa:
examp.
Examp
4
6.
8
10
12
14
16
Figure 5.8
without affecting the meaning of the display.
274

quartile, the median, the third quartile, and the maximum value of the data.
A box-and-whisker diagram (also called a boxplot) is used to display
information of a set of data, including the minimum value, the first
10 selected bottles from filling line A that we have discussed in Section 5.1.
Below is a box-and-whisker diagram for the volumes of soft drink in the
More on Box-and-Whisker
Diagrams
data has a
some
n home to
+
494
502
Volume (mL)
Figure 5.5
496
498
500
504
506
rel time of
The box contains the middle 50% of the data. The median is marked
tr the vertical line segment in the box. The first quartile (Q) and the third
ortile (0,) are marked by the left edge and the right edge of the box,
espectively. The line segments extending from the edges of the box to the
ninimum value and the maximum value are called whiskers. Each whisker
eights of
contains 25% of the data.
median
maximum value
minimum value
25% of data
25% of data 25% of data
Figure 5.6
25% of data
of constructing a box-and-whisker diagram are given below:
steps
The
MATH FOGUE
Draw a box that reaches from the first quartile to the
third quartile on a horizontal scale.
Draw a vertical line segment across the box at the
median.
Step 1.
Step 2.
Draw a line segment from the left edge of the box to
the minimum value.
Siep 3.
Draw a line segment from the right edge of the box to
the maximum value.
Step 4.
273

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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