STATISTICS

1. A study is conducted to determine if the traffic light patterns at a busy intersection need to be

adjusted to help the flow of traffic. Data on the volume of traffic and the traffic patterns during

different times of day are recorded.

2

I. What is the population?

II. What is the sample?

III. Is the study observational or experimental? Justify your answer.

IV. If observational, identify ALL variables. If experimental, identify ALL independent and

dependent variables.

V. For each of the variables identified in part IV, list which of the four levels/scales of

measurement was used to obtain data on these variables?

VI. Classify each of the variables identified in part IV as either attribute or numerical.

Solution

I . Total Flow of the Traffic

II. The volume of Traffic & the patterns that are recorded.

III. It is an experimental study because the objective is to make changes and see how those

changes are effective and evaluate them. Since we are not merely drawing conclusions, it is not

observational.

IV. Variables are

1. Volume of traffic

2. Number of Vehicles

STATISTICS

3. Time

V. Volume of traffic – Ratio

Number of Vehicles – Ratio

Time – Nominal

3

2. Classify the following variable as nominal, ordinal, discrete, or continuous and state why

it is such a variable:

number of MP3 players sold each year

This is a discrete variable because there cannot be a value in decimals here.

3. Classify the following as an example of a nominal, ordinal, interval, or ratio level of

measurement, and state why it represents this level:

distance between two signposts

The distance between the signposts is a ratio level of measurement, because there is a set

definition of 0.0, as in no distance between these signposts. This has all the properties of an

interval variable and has a well defined value of 0.0, therefore such an example is a ratio level of

measurement.

4. Construct a frequency distribution table to organize the following set of data:

STATISTICS

4

101

102

103

105

106

107

108

109

110

2

2

2

1

3

1

2

6

1

5. Construct a grouped frequency distribution for the following 28 scores using a class width of

4:

74 80 79 74 77 64 77 81 63 68 83 71 75 71

70 69 83 71 82 86 77 86 79 75 81 86 78 77

Solution:

Range

63-67

68-72

73-77

78-82

83-87

Frequency

2

6

8

7

5

STATISTICS

6. Provide a different example for each of the following types of variables from your work or

home life:

5

A) A qualitative variable:

A qualitative variable could be the degree of honesty in each of my students during a

tutoring class.

B) A quantitative variable

A quantitative variable could be βheightβ for each of these students.

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