Transcript Glencoe Pre

Over Lesson 13–2
Choose the correct
stem-and-leaf plot for
the table.
A.
B.
3|2 = 32 stories
C.
3|2 = 32 stories
D.
3|2 = 32 stories
3|2 = 32 stories
A.
B.
C.
D.
A
B
C
D
You have already found measures of central
tendency. (Lesson 13–2)
• Find measures of variation.
• Use measures of variation to interpret and
analyze data.
• measures of variation used to describe the
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•
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•
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distribution of statistical data
range a measure of variation that is the difference
between the least and greatest values in a data set
quartiles the values that divide a set of data into four
equal parts
lower quartile the median of the lower half of a set
of data (we use “LQ” for it)
upper quartile the median of the upper half of a set
of data (we use “UQ” for it)
interquartile range the range of the middle half of a
set of data (UQ – LQ)
outlier data that are more than 1.5 times the
interquartile range beyond the quartiles (unusual
values)
Find Range
A. Find the range of the set of data.
Work Time
Stem Leaf
3 335778
4 03349
5 49
3|5 = 35 hours
The greatest value is 59 and the least is 33.
Answer: The range is 59 – 33 or 26 hours.
Find Range
B. Find the range of the set of data.
The cost of jeans at a department store: $79, $42,
$38, $51, $63, $91
The greatest value is $91 and the least is $38.
Answer: The range is $91 – $38 or $53.
A. Find the range of the set of data.
{14, 37, 82, 45, 24, 10, 75}
A. 61
B. 65
C. 68
D. 72
A.
B.
C.
D.
A
B
C
D
B. Find the range of the set of data.
A. 27
B. 20
Stem
5
6
7
Leaf
23559
489
0189
6|8 = 68
C. 18
D. 12
A.
B.
C.
D.
A
B
C
D
Identify Measures of Variation
OLYMPICS Find the measures of variation for the
data in the table.
Step 1 Range: 29 – 14 = 15 medals
Identify Measures of Variation
Step 2 Median, Upper Quartile, Lower Quartile
Order the data from least to greatest.
lower quartile median upper quartile
14
14
19
22
23
24
25
Interquartile range: 24.5 – 16.5 or 8
29
Identify Measures of Variation
Answer: The range is 15. The median is 22.5, the
lower quartile is 16.5 and the upper quartile is 24.5. The
interquartile range is 8.
What are the range (R), interquartile range (IR),
median (M), lower quartile (LQ), and upper quartile
(UQ) for the data in the table?
A.
R: 35, IR: 26, M: 23,
LQ: 14.5, UQ: 40.5
B.
R: 35, IR: 26.5, M: 24,
LQ: 14, UQ: 40.5
C.
R: 32, IR: 26, M: 24,
LQ: 14.5, UQ: 40.5
D.
R: 35, IR: 12.5, M: 23,
LQ: 16, UQ: 28.5
A.
B.
C.
D.
A
B
C
D
Find Outliers
NUTRITION Find any
outliers in the data set.
Step 1 Find the
interquartile range.
lower quartile median
2.5
3
3
4.5
5
upper quartile
5
6
8
The interquartile range is 7 – 3 = 4.
14
Find Outliers
Step 2 Multiply the interquartile range by 1.5.
1.5 ● 4 = 6
Step 3 Subtract 6 from the lower quartile and add 6 to
the upper quartile.
3 – 6 = –3
7 + 6 = 13
Answer: The only outlier is 14 because it is greater
than 13.
Find any outliers in
the data set.
A.
49 is the only outlier.
B.
49 and 15 are outliers.
C.
15 is the only outlier.
D.
There are no outliers.
A.
B.
C.
D.
A
B
C
D
Use Measures of Variation
SOCCER The table shows the number of tickets
sold to soccer games at a local stadium. Use the
measures of variation to describe the data.
Find the measures of variation.
The range is 301 – 98 = 203.
Use Measures of Variation
The interquartile range is 274 – 184 or 90.
Answer: The spread of the data is 203 tickets. The
median number of tickets is 241. The least fourth of the
ticket sales is 184 tickets or less. The greatest fourth of
ticket sales is 274 or more. The number of tickets sold for
half of the games was between 184 and 274.
On the chart below, Mark kept track of the number of
hours he exercised. Which statement is not true?
A. The spread of the data was 1.05
hours.
B. The median number of hours was
0.59 hour.
C. The greatest fourth of time was
0.66 hour or more.
D. The number of hours exercised
for half of the time was between
0.5 hour and 0.66 hour.
A.
B.
C.
D.
A
B
C
D
Measures of Variation
A. LAND USE The urban land in certain Western
and Eastern states is listed below as the percent of
each state’s total land, rounded to the nearest
percent. Compare the western states’ range with
the eastern states’ range.
Western States
4322221
54
2|0 = 2%
Eastern States
0
0 6678
1 0345
2 7
2|7 = 27%
Measures of Variation
Answer: The range for the western states is 4%. The
range for the eastern states is 21%. The
percents of urban land use in the East vary
more.
Measures of Variation
B. LAND USE The urban land in certain Western and
Eastern states is listed below as the percent of each
state’s total land, rounded to the nearest percent.
Does the data for either region contain an outlier?
Western States
4322221
54
2|0 = 2%
Eastern States
0
0 6678
1 0345
2 7
2|7 = 27%
Measures of Variation
Western States
Eastern States
Lower Quartile:
2
6.5
Upper Quartile:
4
14.5
Interquartile Range: 4 – 2 = 2
14.5 – 6.5 = 8
Multiply by 1.5:
2 ● 1.5 = 3
8 ● 1.5 = 12
Determine Outliers: 2 – 3 = –1 x
6.5 – 12 = –5.5 x
4+3=7 x
14.5 + 12 = 26.5 
Answer: There are no outliers for the western states.
Since 27 is greater than 26.5, 27 is an outlier
for the eastern states.
Measures of Variation
C. LAND USE The urban land in certain Western and
Eastern states is listed below as the percent of each
state’s total land, rounded to the nearest percent.
How does the outlier affect the measures of central
tendency for the Eastern States?
Western States
4322221
54
2|0 = 2%
Eastern States
0
0 6678
1 0345
2 7
2|7 = 27%
Measures of Variation
Calculate the mean, median, and mode without the
outlier, 27, in the data for the eastern states.
without the outlier
with the outlier
median: 9
median: 10
mode: 6
mode: 6
Answer: The mean and median are higher with the
outlier. The mode does not change.
A. EXERCISE The hours per week spent
exercising for teenagers and people in
their twenties are listed in the stem-andleaf plot. Compare the range for each set
of data.
A.
teenagers: 21 hr; twenties: 28 hr
The hours of the twenties group vary
more.
B.
teenagers: 15 hr; twenties: 16 hr
The hours of the twenties group vary
only slightly more.
C.
teenagers: 22.5 hr; twenties: 24 hr
The hours of the twenties group vary
only slightly more.
D.
teenagers: 5 hr; twenties: 12 hr
The hours of the twenties group vary
more.
Teens
5420
73
1
3|1 = 13 hr
0
1
2
Twenties
04679
0225
03458
1|5 = 15 hr
A.
B.
C.
D.
A
B
C
D
B. EXERCISE The hours per week Teens
5420 0
spent exercising for teenagers
73 1
and people in their twenties are
1 2
listed in the stem-and-leaf plot.
3|1 = 13 hr
Does the data for either group
contain an outlier?
A. yes; teens
B. yes; twenties
C. yes; both groups contain an
outlier.
D. No; neither group contains an
outlier.
Twenties
04679
0225
03458
1|5 = 15 hr
A.
B.
C.
D.
A
B
C
D