Transcript AP Stats Test Review #2

AP Stats Test Review #2
Focus:
Measures of Center and Spread
Outliers
Boxplots
Experiments
Random Variables
Measures of Center and Spread
Measures of Center are Mean and
Median

Median is resistant to outliers (chop
the outliers off)
 Mean is non-resistant to outliers
(better measure for approximately
normal distributions)
Measures of Spread are IQR and
Standard Deviation
 IQR goes with Median and Standard
Deviation goes with Mean
Outliers
Outliers are all data that are more than 1.5
IQR from Q1 and Q3.
Outliers
 Q1  1.5( IQR)
 Q3  1.5( IQR)
Boxplots
Boxplots are displays that show the 5 number
summary
Minimum
Q1
Median
Q3
Maximum
Modified boxplots
exclude the outliers.
10 14 16 17 19 21 13 18 18
19 20 16 18 21 23 18 24 3
1) Find the measures of center and spread,
2) If 5 was added to each piece of data, what would the new
measures of center and spread be?
3) If each piece of data was multiplied by 10, what would the
new measures of center and spread be?
4) Calculate if there are any outliers in the data set.
5) Draw a modified boxplot for the data.
10
14
16
17
19
21
13
18
18
19
20
16
18
21
23
18
24
3
Answers:
1) x  17.11, sx  4.91, M  18, IQR  4
The median and IQR is more appropriate because data is
skewed.
2) x  22.11, sx  4.91, M  23, IQR  4
3) x  170.11, sx  40.91, M  180, IQR  40
4) IQR = 20 – 16 = 4  1.5(IQR) = 6
Q1 – 6 = 16 – 6 = 10  since 3 is less than 10, it is an
outlier.
Q3 + 6 = 20 + 6 = 26  no data is over 26, so no
outliers on this side.
Experiments
An experiment is when a treatment is
imposed. A study is when you observe a
behavior (no treatment).
In an experiment, you want to use a control or
placebo when appropriate. Why?
The Principles of Experiments are:
1) Control
2) Randomize
3) Replicate
4) Block when possible to reduce lurking
variables
What is the definition of each term?
Blinding (Single or Double)
Level
Factors
Response variable
Blinding (Single or Double) – Not allowing
the subjects and/or evaluators to know who
is assigned to what treatment.
Level – A variable whose values are controlled
by the experimenter. (i.e. 400 mg, 800
mg, 1200 mg of aspirin)
Factors – all the different treatments
Response variable – the variable that is
affected by the treatments (i.e. losing
weight because of treatments)
You are interested in determining if daily
doses of ibuprofen reduces the pain of
arthritis in elderly people. You have 60
elderly people with arthritis who are
willing to volunteer. In addition, you
are going to administer 2 different
doses of ibuprofen, 400 mg and 800
mg. You are also unsure if gender is a
factor in the effectiveness of ibuprofen
on arthritis. Design an experiment
that takes all of these variables into
account.
Random Variables
X
P(x)
$3
.25
$5
.10
$8
.40
$0
.25
A game is played by spinning a spinner with the values
$3, $5, $8 and $0 with the following probabilities.
What is the expected value and standard deviation of
the winning?
u x  ( xi p( xi )
  ( xi   )² p( xi )
2
x
Answers:
Expected value = $4.45
Standard Deviation = $3.25
What happens when you add and
subtract random variables?
 x y   x   y

2
x y
  
2
x
2
y
 x y   x   y

2
x y
  
2
x
2
y
Last Example
The mean number of bolts needed to
make a truck is 321 with a standard
devation of 15 and the mean number
of switches to build a truck is 23 with
a standard deviation of 6. Find:
a) the mean and standard deviation of
bolts and switches to build one truck.
b) the mean and standard deviation of
bolts needed to make 3 trucks.
Answers:
a )u x  y  321 23  344

2
x y
 15²  6²  261
 x  y  261  16.16
b)u3 x  3(321)  963
 3 x  15²  15²  15²  25.98