Learn to find measures of variability.

1
Box-and-whisker Plots
Learn to find measures of variability.
2
The range of a data set is the largest value
minus the smallest value.
The table below summarizes a veterinarians
records for kitten litters born in a given year.
Litter Size 2 3 4 5 6
Number of Litters 1 6 8 11 1
While central tendency describes the middle of a
data set, variability describes how spread out
the data is.
Quartiles divide a data set into four equal
parts.
3
The range of a data set is the largest value
minus the smallest value. For the kitten data,
the range is 6 2 4.
Kitten Data
Lower half
Upper half
2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5
5 6
Litter Size 2 3 4 5 6
Number of Litters 1 6 8 11 1
The range is affected by outliers, so another
measure is often used. Quartiles divide a data
set into four equal parts.
4
A box-and-whisker plot shows the distribution of
data. The middle half of the data is represented
by a box with a vertical line at the median.
The lower fourth and upper fourth quarters are
represented by whiskers that extend to the
smallest and largest values.
Median
First quartile
Third quartile
5
Try This
Use the given data to make a box-and-whisker
plot. 31, 23, 33, 35, 26, 24, 31, 29
Step 1. Order the data and find the smallest
value, first quartile, median, third quartile,
and largest value.
23 24 26 29 31 31 33 35
smallest value 23
largest value 35
6
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above
each value.
23 24 26 29 31 31 33 35
7
Use the given data to make a box-and-whisker plot.
Step 3. Draw the box and whiskers.
Step 2. Draw a number line and plot a point above
each value.
23 24 26 29 31 31 33 35
8
Finding Measures of Variability
Find the range and the first and third quartiles
for the data set.
A. 15, 83, 75, 12, 19, 74, 21
Order the values.
12 15 19 21 74 75 83
range 83 12 71
first quartile 15
third quartile 75
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Finding Measures of Variability
Find the range and the first and third quartiles
for the data set.
B. 75, 61, 88, 79, 79, 99, 63, 77
Order the values.
61 63 75 77 79 79 88 99
range 99 61 38
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Making a Box-and-Whisker Plot
Use the given data to make a box-and-whisker
plot 21, 25, 15, 13, 17, 19, 19, 21
Step 1. Order the data and find the smallest
value, first quartile, median, third quartile,
and largest value.
13 15 17 19 19 21 21 25
smallest value 13
largest value 25
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Continued
Use the given data to make a box-and-whisker plot.
Step 1. Order the data and find the smallest
value, first quartile, median, third quartile,
and largest value.
Step 2. Draw a number line and plot a point above
each value from step 1.
13 15 17 19 19 21 21 25
smallest value 13
first quartile 16
third quartile 21
median 19
largest value 25
12
Continued
Use the given data to make a box-and-whisker plot.
Step 2. Draw a number line and plot a point above
each value.
Step 3. Draw the box and whiskers.
13 15 17 19 19 21 21 25
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Lesson Quiz
Use the following data for problems 3 and 4. 91,
87, 98, 93, 89, 78, 94 1. Make a
box-and-whisker plot 2. What are the 3
quartiles?
87, 91, 94