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6-3 Measures of Variation
I CAN make a box-and-whisker plot. I
CAN find the interquartile range of a set
of numbers. I CAN find the mean
absolute deviation of a set of numbers.
6-3 Measures of Variation
Vocabulary
box-and-whisker plot
quartiles
variation
interquartile range (IQR)
mean absolute deviation
6-3 Measures of Variation
Ms. Snow asks some of her students how many pets
they have. The responses are 9, 0, 4, 1, 1, 2, 3, 5,
and 2 pets.
You can display this data using a box-and-whisker
plot. A box-and-whisker plot or box plot is a data
display that shows how data are distributed by
using the median, quartiles, least value, and
greatest value.
Quartiles are three values, one of which is the
median, that divide a data set into fourths. Each
quartile contains one-fourth, or 25%, of the
data.
6-3 Measures of Variation
Example 1: Making a Box-and-Whisker Plot
The average number of hours that several
students watch television in a day is given. Use
the data to make a box-and-whisker plot: 2, 1,
5, 2, 1, 2, 3, 2, 2.
Step 1 Order the data from least to greatest.
1, 1, 2, 2, 2, 2, 2, 3, 5
Step 2 Find the least and greatest values, the
median, and the first and third quartiles.
1
1
2
2
2
2
2
3
5
Greatest Value
Least value
First Quartile
Median
1.5
Third Quartile
2.5
6-3 Measures of Variation
Continued: Example 1
Step 3
Draw a number line, and plot a point above each of
the five values you just identified. Draw a box
through the first and third quartiles and a vertical line
through the median. Draw lines from the box to the
least value and the greatest value. (These are the
whiskers.)
0
1
2
3
4
5
6
6-3 Measures of Variation
You Try! Example 1
The next 9 customers in line are waiting to
purchase the following number of items: 6, 10,
8, 5, 9, 4, 10, 7, 5. Use the data to make a boxand-whisker plot.
Step 1 Order the data from least to greatest.
4, 5, 5, 6, 7, 8, 9, 10, 10
Step 2 Find the least and greatest values, the
median, and the first and third quartiles.
4
5
5
6
7
8
9
10 10
Greatest Value
Least value
First Quartile
5
Median
Third Quartile
9.5
6-3 Measures of Variation
Continued: You Try! Example 1
Step 3
Draw a number line, and plot a point above
each of the five values you just identified. Draw
a box through the first and third quartiles and a
vertical line through the median. Draw lines
from the box to the least value and the greatest
value. (These are the whiskers.)
0
1
2
3
4
5
6
7
8
9
10 11
6-3 Measures of Variation
CAN YOU make a box-and-whisker plot?
6-3 Measures of Variation
Lesson Quiz
A park ranger measures the thickness of ice on a
lake in 8 different locations: 19 in., 17 in., 15 in.,
15 in., 18 in., 12 in., 16 in., 14 in.
Make a box-and-whisker plot of the data.
6-3 Measures of Variation
HOMEWORK
6-3 Measures of Variation
A box-and-whisker plot can be used to show how the
values in a data set are distributed. Variation
(variability) is the spread of the values.
The interquartile range (IQR) is the difference
between the first and third quartiles. It is a
measure of the spread of the middle 50% of the
data.
A small interquartile range means that the data in the
middle of the set are close in value. A large
interquartile range means that the data in the middle
are spread out.
6-3 Measures of Variation
Example 2: Finding the Interquartile Range
Find the interquartile range for the data set 17,
39, 38, 9, 29, 40, 27
9, 17, 27, 29, 38, 39, 40 Order the data from least to
greatest.
9,
17,
27,
29, 38,
IQR=39-17=22
39,
40
Find the median and quartiles
Find the difference between the
first quartile (17) and the third
quartile (39).
The interquartile range is 22.
6-3 Measures of Variation
You Try! Example 2
Find the interquartile range for the data set 87,
71, 72, 73, 84, 92, 73.
71, 72, 73, 73, 84, 87, 92 Order the data from least to
greatest.
71,
72, 73,
73, 84,
IQR=87-72=15
87,
92
Find the median and quartiles
Find the difference between the
first quartile (72) and the third
quartile (87).
The interquartile range is 15.
6-3 Measures of Variation
Another measure of variation is the mean
absolute deviation. Mean absolute deviation is
the mean amount that data values differ
from the mean of the data values.
6-3 Measures of Variation
Example 3: Finding Mean Absolute Deviation
A scientist is studying temperature variation.
She determines that the temperature at noon
on four days is 75F, 82F, 78F, and 67F.
What is the mean absolute deviation of the
temperatures?
Find the mean.
.
75+82+78+67 = 75.5
4
75 is 0.5 unit from 75.5.
82 is 6.5 units from 75.5.
78 is 2.5 units from 75.5.
67 is 8.5 units from 75.5.
Find the mean
Find the distance on a
number line each data value
is from the mean. each data
value is from the mean.
6-3 Measures of Variation
Continued: Example 3
0.5+6.5+2.5+8.5
4
= 4.5. Find the mean of the
distances
The mean absolute deviation of the temperatures
is 4.5F. So, on average, the temperatures were
within 4.5F of the mean, 75.5F.
6-3 Measures of Variation
You Try! Example 3
A scientist is studying temperature variation.
She determines that the temperature at noon
on four days is 64F, 75F, 80F, and 78F.
What is the mean absolute deviation of the
temperatures?
Find the mean.
64+75+80+78 = 74.25
4
64 is 10.25 units from 74.25.
75 is 0.75 unit from 74.25.
80 is 5.75 units from 74.25.
78 is 3.75 units from 74.25.
Find the mean
Find the distance on a
number line each data value
is from the mean.
6-3 Measures of Variation
Continued: You Try! Example 3
Find the mean of the distances
10.25+0.75+5.75+3.75 = 5.125.
4
The mean absolute deviation of the temperatures is
5.125F. So, on average, the temperatures were
within is 5.125F of the mean, 74.25F.
6-3 Measures of Variation
CAN YOU find the interquartile range for a
set of numbers? CAN YOU find the mean
absolute deviation for a set of numbers?
6-3 Measures of Variation
Lesson Quiz
A park ranger measures the thickness of ice on a
lake in 8 different locations: 19 in., 17 in., 15 in.,
15 in., 18 in., 12 in., 16 in., 14 in.
1. Find the interquartile range of the data.
3 in.
2. Find the mean absolute deviation of the data.
1.75 in.
6-3 Measures of Variation
HOMEWORK