Transcript Box-and-Whisker Plot

Box-and-Whisker Plots
• We have learned various ways of
organizing data so far.
• We have learned
– Line graphs
– Bar Graphs
– Tables
• Next we will learn Box-and-Whisker Plots.
Box-and-Whisker Plots
• Vocabulary
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Box-and-Whisker Plot
Upper Quartile (UQ)
Lower Quartile (LQ)
Median
Upper Extreme
Lower Extreme
Interquartile range
Box-and-Whisker Plots
• So what is a box and whisker plot?
• A visual way to see the biggest number, lowest
number, median of the set, median of the upper half
of a set, and the median of the lower half of a set.
• We will use a Box and lines extending from the box
(whiskers) to show these values.
Box-and-Whisker Plots
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To make a box-and-whisker plot, I need 5
things. (Before finding these, always put the data in order first.)
Upper Extreme (UE)
Lower extreme (LE)
Median
Upper Quartile (UQ)
Lower Quartile (LQ)
Five Values needed to make a
Box-and-Whisker Plot
1. Upper Extreme- the largest value in a set of data.
2. Lower Extreme – the smallest value in a set of
data.
Ex. In the set 1,2,3,4,5,6,7; what is the upper
extreme and the lower extreme?
Upper Extreme: 7
Lower Extreme: 1
Five Values needed to make a
Box-and-Whisker Plot
3. Median – Middle number when the values
are written from least to greatest.
4. Upper Quartile (UQ) – When the values of
a set are split into two groups by the
median, the median of the upper half is
called the upper quartile.
Example of Median
• The median of this set of numbers is the number in the
middle when the numbers are written in order.
1,2,3,4,5,6,7
• So what is the median of:
1,2,3,4,5,6,7
• So 4 is the median for our data set.
Example of Upper Quartile
• Ex. Set of data: 1,2,3,4,5,6,7
• The numbers are written from least to greatest. The middle value is 4,
so 4 is the median.
• So 4 splits the numbers in half.
• So now I cover up the median and look at all values to the RIGHT (the
upper half).
• 1,2,3,4,5,6,7
• The median of the values to the right of the median is called the upper
quartile (UQ).
• So what is the median of 5,6,7? 6
• So 6 is the upper quartile (UQ) for our data set.
Five Values needed to make a
Box-and-Whisker Plot
5. Lower Quartile (LQ)- When the values of
a set are split into two groups by the
median, the median of the lower half is
called the lower quartile.
Example of Lower Quartile (LQ)
• Ex. Set of data: 1,2,3,4,5,6,7
• The numbers are written from least to greatest. The middle
value is 4, so 4 is the median.
• So 4 splits the numbers in half.
• So now I cover up the median and look at all values to the
LEFT (the lower half).
• 1,2,3,4,5,6,7
• The median of the values to the right of the median is
called the upper quartile (UQ).
• So what is the median of 1,2,3? 2
• So 2 is the Lower Quartile (LQ) for our data set.
Five Values needed to make a
Box-and-Whisker Plot
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So now we have all five necessary items for our
data set: 1,2,3,4,5,6,7
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2.
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5.
Upper Extreme = 7
Lower extreme = 1
Median = 4
Upper Quartile (UQ) = 6
Lower Quartile (LQ) = 2
Box-and-Whisker Plot
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Interquartile Range
• Interquartile Range – subtract the lower quartile
(left side of the box) from the upper quartile (right
side of the box).
• [UQ (right side of box )] – [LQ (left side of the box )]
Example for our data
UQ = 6
LQ = 2
Interquartile range = UQ – LQ = 6 – 2 = 4
Box-and-Whisker Plot (Practice #1)
2, 4, 6, 8, 10, 12, 14, 16
UE =
LE =
Median =
16
2
9
UQ =
13
LQ =
5
Create the box-and-whisker plot on your
sheet.
Box-and-Whisker Plot (Practice #2)
12, 15, 24, 31, 38, 39, 42, 50, 50
UE =
LE =
Median =
50
12
38
UQ =
46
LQ =
19.5
Create the box-and-whisker plot on your
sheet.