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…

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

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 = ______Std Dev = ______

Variance = ______

Is Boardwalk’s rent “unusual”? Explain.

Introduction to Statistics and Data Analysis

Quartles, IQR, and Boxplots

Part I. Match the histogram to the corresponding boxplot.

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 / 44 / 35 / 80 / 26 / 28 / 41 / 21 / 61 / 38 / 49 / 33 / 74
30 / 33 / 41 / 31 / 35 / 41 / 42 / 37 / 26 / 34 / 34 / 35 / 26
61 / 60 / 34 / 24 / 30 / 37 / 31 / 27 / 39 / 34 / 26 / 25 / 33

**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.

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 Hips / Barbie
Chest Waist Hips
Doll / 75.0 / 56.5 / 72.0 / 82.3 / 40.7 / 72.7
Human / 91.2 / 80.9 / 93.7 / 90.3 / 69.8 / 97.9
Human / 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 withan 79.2 cm or larger waist?