Warm Up

1
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
2
Warm Up 1. Order the test scores from least to
greatest 89, 93, 79, 87, 91, 88, 92. 2.
Find the median of the test scores. Find the
difference.
79, 87, 88, 89, 91, 92, 93
89
3. 17 0.9 4. 8.4 7. 6
16.1
0.8
3.4
166.9
5. 9.1 5.7 6. 190.3 23.4
3
Problem of the Day What are the possible values
for x in the data set 22, 12, 33, 25, and x if
the median is 25?
any number greater than or equal to 25
4
Sunshine State Standards
MA.8.S.3.1 Constructbox-and-whisker plotsto
convey information and make conjectures about
possible relationships.
5
Vocabulary
variability box-and-whisker plot first
quartile third quartile interquartile range
6
While central tendency describes the middle of a
data set, variability describes how spread out
the data are. A box-and-whisker plot uses a
number line to show how data are distributed and
to illustrate the variability of a data set. A
box-and-whisker plot divides the data into four
parts. The median, or second quartile, divides
the data into a lower half and an upper half. The
first quartile is the median of the lower half of
the data, and the third quartile is the median of
the upper half of the data.
7
(No Transcript)
8
Additional Example 1 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 least value,
first quartile, median, third quartile, and
greatest value.
13 15 17 19 19 21 21 25
least value 13
greatest value 25
9
Additional Example 1 Continued
Step 2 Draw a number line and plot a point above
each value from Step 1.
13 15 17 19 19 21 21 25
least value 13
first quartile 16
third quartile 21
greatest value 25
median 19
10
Additional Example 1 Continued
Step 3 Draw the box and whiskers.
13 15 17 19 19 21 21 25
11
Check It Out Example 1A
Use the given data to make a box-and-whisker
plot. 31, 23, 33, 35, 26, 24, 31, 29
23 25 30 32 35
12
Check It Out Example 1B
Use the given data to make a box-and-whisker
plot. 57, 53, 52, 31, 48, 58, 64, 86, 56, 54, 55
13
The interquartile range of a data set is the
difference between the third quartile and the
first quartile. It represents the range of the
middle half of the data.
14
Additional Example 2 Using Interquartile Range
to Identify Outliers
Use interquartile range to identify any
outliers. 75, 65, 78, 79, 76, 79, 72, 82
Step 1 Determine the first quartile, the third
quartile, and the interquartile range.
65 72 75 76 78 79 79 82
Q1 73.5
Q3 79
IQR 79 73.5 5.5
15
Additional Example 2 Continued
Use interquartile range to identify any
outliers. 75, 65, 78, 79, 76, 79, 72, 82
Step 2 Determine whether there is an outlier
less than the first quartile.
Q1 (1.5 ? IQR)
73.5 (1.5 ? 5.5)
73.5 8.25 65.25
The least value in the data set is 65. This value
is less than 65.25.
16
Additional Example 2 Continued
Use interquartile range to identify any
outliers. 75, 65, 78, 79, 76, 79, 72, 82
Step 3 Determine whether there is an outlier
greater than the third quartile.
Q3 (1.5 ? IQR)
79 (1.5 ? 5.5)
79 8.25 87.25
The greatest value in the data set is 82. None of
the values are greater than 87.25.
17
Additional Example 2 Continued
Use interquartile range to identify any
outliers. 75, 65, 78, 79, 76, 79, 72, 82
The data value 65 is an outlier.
18
Check It Out Example 2A
Use the interquartile range to identify any
outliers. 25, 12, 31, 26, 27, 29, 32
12, 25, 26, 27, 29, 31, 32
Q1 25
Q3 31
IQR 31 25 6
Q1 (1.5 IQR) 25 (1.5)(6)
25 9 16
19
Check It Out Example 2A Continued
Use the interquartile range to identify any
outliers. 25, 12, 31, 26, 27, 29, 32
12 is less than 16, so 12 is an outlier. No
values are greater than 40, so there are no other
outliers.
20
Check It Out Example 2B
Use the interquartile range to identify any
outliers. 35, 46, 50, 32, 54, 44, 40
32, 35, 40, 44, 46, 50, 54
Q1 35
Q3 50
IQR 50 35 15
Q1 (1.5 IQR) 35 (1.5)(15)
35 22.5 12.5
21
Check It Out Example 2B Continued
Use the interquartile range to identify any
outliers. 35, 46, 50, 32, 54, 44, 40
Q3 (1.5 IQR) 50 (1.5)(15)
50 22.5 72.5
No values are less than 12.5 or greater than
72.5, so there are no outliers.
22
Additional Example 3 Comparing Data Sets Using
Box-and-Whisker Plots
Note 57 is the first quartile and the median.
These box-and-whisker plots compare the ages of
the first ten U.S. presidents with the ages of
the ten presidents from Dwight Eisenhower through
George W. Bush when they took office.
23
Additional Example 3 Continued
Note 57 is the first quartile and the median.
A. Compare the medians and ranges.
The median for the first ten presidents is
slightly greater. The range for the last ten
presidents from 1953-2008 is greater.
24
Additional Example 3 Continued
Note 57 is the first quartile and the median.
B. Compare the interquartile ranges.
The interquartile range is greater for the ten
presidents from 1953-2008.
25
Check It Out Example 3
Compare the interquartile ranges of the data sets
in Example 3.
For the first ten presidents IQR 61 57 4
For the ten presidents from 19532008 IQR 62
52 10
The interquartile range is greater for the ten
presidents from 19532008.
26
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
27
Lesson Quiz Part I
Use the following data for problems 1 and 2. 91,
87, 98, 93, 89, 78, 94 1. Make a
box-and-whisker plot. 2. Use the interquartile
range to identify and outliers.
none
28
Lesson Quiz Part II
3. Use the box-and-whisker plots to compare the
medians and ranges of the data sets.
Data set A has a greater median. Data set B has a
greater range.
29
Lesson Quiz for Student Response Systems
1. Identify the first and third quartiles for the
given data set. 15, 45, 65, 75, 35, 55, 25 A.
Q1 15 Q3 65 B. Q1 25 Q3 65 C. Q1 15
Q3 75 D. Q1 25 Q3 75
30
Lesson Quiz for Student Response Systems
2. Identify a box-and-whisker plot for the given
data. 42, 72, 65, 44, 52, 79, 68, 55, 60 A.
B.