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Lesson
Compare datas
Outliers
• A data value is an outlier if x < Q1 – 1.5(IQR) or
• if x > Q3 + 1.5(IQR)
• Statistics – numbers that characterize a data
set, such as measures of center and spread.
Performance Task p 400
Dealer A
Dealer B
14
13
15
12
16
17
15
20
15
16
15
17
18
19
18
17
17
12
16
14
19
10
19
18
15
16
14
16
15
17
20
19
13
14
18
15
18
18
16
17
The tables list the daily car sales of two
competing dealerships.
A. Calculate the mean, median,
interquartile range (IQR), and
standard deviation for each data
set. Compare the measures of
center for the two dealers.
mean
Dealer A
Dealer B
median
IQR
Standard
Deviation
mean
median
IQR
Standard
Deviation
Dealer A
14.85
15
2
1.6
Dealer B
17.3
18
2.5
2.2
Answer
• The number of cars sold by Dealer A tends to
be lower than the number of cars sold by
Dealer B.
• The number of cars sold by Dealer A are more
consistent than the number of cars sold by
Dealer B
B. Create a dot plot for each data set.
Compare the distributions of the data
sets.
Answers
• The data for Dealer A show a symmetric
distribution, so the number of cars sold daily
by Dealer A is evenly distributed about the
mean.
• The data for Dealer B show a distribution
skewed to the right, so during more than half
of the days, car sales were greater than the
mean.
C. Determine if there are any outliers
in the data sets. If there are, remove
the outlier and find the statistics for
that data set(s).
What was affected by the outliers?
answer
•
•
•
•
Dealer A
x < 14 – 1.5 (2)
x > 16 + 1.5(2)
x < 11
x > 19
There are no values in the data set that satisfy
this inequalities for x. So, there are no outliers
•
•
•
•
•
Dealer B
x < 16.5 – 1.5 (2.5)
x > 19 + 1.5(2.5)
x < 12.75
x > 22.75
10 is an outlier in the data set for Dealer B.
Removing the outlier increases the mean and
decreases the std dev. The median is
unaffected