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.
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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
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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:
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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 βheightβ for each of these students.