Mid Chapter Review 4.1 to 4.4A
Measures of Typical Value (Center)
Part I. For each data set given below, do the following:




Construct a dotplot of the data.
Describe the shape of the dotplot.
Compute the mean and mark its place on the number line of your dotplot.
Compute the median and mark its place on the number line of your dotplot.
For example…
The doptlot is unimodal and symmetric.
There are no outliers.
0
1
2
3
Mean = 2.00 Median = 2.00
Data Set #1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Data Set #2: 1, 1, 1, 2, 3, 8, 9, 10, 10, 10
4
Data
Data Set #3: 0, 0, 0, 0, 0, 1, 1, 1, 2, 3
Data Set #4: 0, 17, 18, 18, 19, 19, 19, 19, 20, 20
Part II. Answer each of the following questions…
A. When are the mean and the median equal?
B. When is the mean greater than the median?
C. When is the mean less than the median?
D. When is a “typical” value of the data set best represented by the mean? By the median?
Part II. The twenty-two properties on a Monopoly board, and their respective rents, are listed in the
table below.
**Enter the rents into a list in your calculator.**
1. Construct and draw a histogram of the rents.
Describe the distribution.
2. Compute the mean and standard deviation for the rents. This data set is the entire population
of Monopoly rents. Use appropriate notation for each parameter.
Mean = ________
Variance = ___________
Is Boardwalk’s rent “unusual”? Explain.
Std Dev = ________
Introduction to Statistics and Data Analysis
Quartles, IQR, and Boxplots
Part I. Match the histogram to the corresponding boxplot.
Histogram #1
Histogram #2
40
12
30
8
Frequency
Frequency
10
6
20
4
10
2
0
0
10
20
30
40
50
X
60
70
80
90
0
100
0
10
20
30
Histogram #3
40
50
X
60
70
80
90
100
70
80
90
100
70
80
90
100
70
80
90
100
Histogram #4
35
20
30
25
Frequency
Frequency
15
10
20
15
10
5
5
0
0
10
20
30
40
50
X
60
70
80
90
100
0
0
10
20
30
Boxplot A
0
10
20
30
40
50
X
60
10
20
30
40
50
X
60
50
X
60
Boxplot B
70
80
90
100
0
10
20
30
Boxplot C
0
40
40
50
X
60
Boxplot D
70
80
90
100
0
10
20
30
40
50
X
60
Part II. The table below contains the ages at which Oscar winning actresses won their awards (“Ages of
Oscar-Winning Best Actors and Actresses”, Richard Brown and Gretchen Davis, Mathematics Teacher
magazine).
50
30
61
44
33
60
35
41
34
80
31
24
26
35
30
28
41
37
41
42
31
21
37
27
61
26
39
38
34
34
49
34
26
33
35
25
**Enter the data into a list in your calculator. **
1. Obtain the five-number summary. (Stat,Calc, then 1-Var Statistics)
2. Compute the IQR.
3. Compute the missing values below:
For the actresses, values below ________ OR above ________ are considered to be outliers.
4. a. Draw a *modified* boxplot below.
Describe the distribution.
74
26
33
In recent years there has been considerable discussion about the appropriateness of the body
shapes and proportions of Ken and Barbie dolls. These dolls are very popular, and there is some
concern that the dolls may be viewed as having the "ideal body shape," potentially leading young
children to risk anorexia in pursuit of that ideal. Researchers investigating the dolls' body shapes
scaled Ken and Barbie up to a common height of 170.18 cm (5' 7") and compared them to body
measurements of active adults. Common measures of body shape are the chest (bust), waist, and
hip circumferences. These measurements for Ken and Barbie and their reference groups are
presented in the table below:
Doll and Human Reference Group Measurements (cm)
Ken
Chest
Waist
Barbie
Hips
Chest
Waist
Hips
Doll
75.0
56.5
72.0
82.3
40.7
72.7
Human x
91.2
80.9
93.7
90.3
69.8
97.9
Human s
4.8
9.8
6.8
5.5
4.7
5.4
For the following questions, suppose that the researchers' scaled up dolls suddenly found
themselves in the human world of actual men and women.
(a) Convert Barbie's chest, waist, and hips measurements to z-scores. Which of those
measures appears to be the most different from Barbie's reference group? Justify your response
with an appropriate statistical argument.
(b) If women's waist measurements are normally distributed, based on the sample above what is the
approximate percent of a woman with an 79.2 cm or larger waist?