1. Data set basics - Elements, variables, observations, measurements, and data types
An analyst collected data on some of the specifications for new vehicles produced for the 2004 model year.
The top and bottom portions of the data set are reproduced below; dots indicate that the intervening rows in the data set are not displayed. (Source: Roger W. Johnson, Journal of Statistics Education Data Archive)
|
Vehicle ID
|
Drive Train
|
Price
|
Engine Size (Liters)
|
City Miles per Gallon
|
Weight (Pounds)
|
|
1
|
1
|
$11,690
|
1.6
|
28
|
2,370
|
|
2
|
1
|
$12,585
|
1.6
|
28
|
2,348
|
|
3
|
1
|
$14,610
|
2.2
|
26
|
2,617
|
|
4
|
1
|
$14,810
|
2.2
|
26
|
2,676
|
|
5
|
1
|
$16,385
|
2.2
|
26
|
2,617
|
|
.
|
.
|
.
|
|
|
.
|
|
.
|
.
|
.
|
|
|
.
|
|
.
|
.
|
.
|
|
|
.
|
|
424
|
0
|
$26,650
|
5.6
|
14
|
5,287
|
|
425
|
0
|
$24,520
|
2.5
|
21
|
3,485
|
|
426
|
2
|
$12,800
|
2.4
|
22
|
2,750
|
|
427
|
2
|
$16,495
|
3.4
|
16
|
3,925
|
|
428
|
0
|
$25,935
|
3.4
|
14
|
4,435
|
Note that the variable Drive Train has three different values, which are coded as 0 = all-wheel drive, 1 = front-wheel drive, and 2 = rear-wheel drive.
Complete the table below to indicate the number of elements, variables, observations, and data values that are included in the complete data set.
Data Set Term How Many?
|
Elements
Variables
Observations
Measurements
|
1
|
|
|
|
1
|
|
|
|
1
|
|
1
|
|
|
a. Which variables in the data set are quantitative?
- Price, Engine Size, City Miles per Gallon, and Weight
- None of the variables
- All of the variables
- Drive Train
2. Identifying the measurement scale of data
Researchers studied how accurately a movie's box office gross can be predicted before its release. [Source: Simonoff, J. S., & Sparrow, I. R. (2000). Predicting movie grosses: Winners and losers, blockbusters and sleepers. Chance, 13(3), 15-25.]
For a sample of movies, data were collected on the following variables:
• Box Office Revenue (in dollars)
• Runtime (in minutes)
• Genre (1 = action, 2 = children's, 3 = comedy, 4 = documentary, 5 = drama, 6 = horror, 7 = science fiction, 8 = thriller)
• Production Budget (in dollars)
• Sequel (0 = not a sequel, 1 = sequel)
Recognizing the measurement scale of the data collected on each variable is important because the type of data dictates the appropriate data summary methods and statistical procedures.
a. Which variable(s) in the data set are measured using a nominal scale?
Sequel
Genre
Genre and Sequel
None of the variables
b. Which variable(s) in the data set are measured using an ordinal scale?
Sequel
Genre
Genre and Sequel
None of the variables
c. Which variable(s) in the data set are measured using a ratio scale?
Box Office Revenue and Production Budget
Runtime
None of the variables
Box Office Revenue, Runtime, and Production Budget