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AP STATISTICS
Day 13
1)
Complete Assignment From Yesterday
-Construct the following:
-histogram
-center, shape, spread, outliers
-ogive
-stemplot
-use split stems
-center, shape, spread, outliers
-dotplot
-center, shape
-boxplot
-five-number summary
2)
Mean vs. Median
-College recruiter offering jobs
-Interview with a college recruiter for small marketing firm
-States that average salary is $80,000
-Five people in office each make $32,000
-Owner makes $320,000
-Mean vs. Median argument
-Mean
-Use when data is symmetric
-Median
-Use when data is skewed
3)
Mode vs. Median vs. Mean
-Use density curves below
4)
Standard Deviation
-Measures how far each value is from the mean
-Measures variation of data
-Pick 6 students and ask number of minutes they drive to school
-Use data with powerpoint slides 23-27
5)
Symmetric
-If the shape is symmetric, report the mean and standard deviation and possibly the median and
IQR. The fact that the mean and median do not agree is a sign that the distribution may be
skewed.
-If the shape is skewed, report the median and IQR. You may want to include the mean and
standard deviation, but you should point out why the mean and median differ. The fact that the
mean and median do not agree is a sign that the distribution may be skewed.
-If there are clear outliers and you are reporting the mean and standard deviation, report them
with the outliers present and with the outliers removed. The differences may be revealing.
6)
Assignment
-Pages 90-91/5-9,11
Skewness
What About Spread? The Standard Deviation


A more powerful measure of spread than the IQR
is the standard deviation, which takes into
account how far each data value is from the
mean.
A deviation is the distance that a data value is
from the mean.
 Since adding all deviations together would total
zero, we square each deviation and find an
average of sorts for the deviations.
Slide 5- 1
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
What About Spread? The Standard Deviation
(cont.)

The variance, notated by s2, is found by summing
the squared deviations and (almost) averaging
them:
s2 

 y  y 
2
n 1
The variance will play a role later in our study, but
it is problematic as a measure of spread—it is
measured in squared units!
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5- 24
What About Spread? The Standard Deviation
(cont.)

The standard deviation, s, is just the square root
of the variance and is measured in the same
units as the original data.
s
 y  y 
2
n 1
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5- 25
Thinking About Variation




Since Statistics is about variation, spread is an
important fundamental concept of Statistics.
Measures of spread help us talk about what we
don’t know.
When the data values are tightly clustered around
the center of the distribution, the IQR and
standard deviation will be small.
When the data values are scattered far from the
center, the IQR and standard deviation will be
large.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5- 26
Shape, Center, and Spread

When telling about a quantitative variable, always
report the shape of its distribution, along with a
center and a spread.
 If the shape is skewed, report the median and
IQR.
 If the shape is symmetric, report the mean and
standard deviation and possibly the median
and IQR as well.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5- 27