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Course textbook: Elementary Statistics: A Step By Step Approach, by Bluman, 7th Edition

Exercise 2–3: Problem 14

14. State which graph (Pareto chart, time series graph, or pie graph) would most appropriately represent the given situation. Explain your answer in a brief description.

a. The number of students enrolled at a local college for each year during the last 5 years.

This is best as a time series graph, since that will let us see the trend in number of students over the time period.

b. The budget for the student activities department at a certain college for each year during the last 5 years.

This is best as a time series graph, since that will let us see the trend in the budget over the time period.

c. The means of transportation the students use to get to school.

This would be a good application for a pie chart. It would allow the user to visually see which types of transportation are the most popular.

d. The percentage of votes each of the four candidates received in the last election.

This would be good as a pie graph, since it will quickly let us compare how each of the candidates did in the election.

e. The record temperatures of a city for the last 30 years.

This is best as a time series graph, since that will let us see the trend in the record temperatures over the time period.

f. The frequency of each type of crime committed in a city during the year.

This could be a good pareto chart, since there are probably lots of different crimes, so a pie chart wouldn’t have room to show them all.

Review Exercise 7

7. Classify each as nominal-level, ordinal-level, interval level, or ratio-level measurement.

a. Pages in the city of Cleveland telephone book.

This is ratio data. There is a clear numeric meaning to the number of pages, and if a book has 100 pages, that is truly twice as many pages as a 50 page book. Since ratios are meaningful, this is ratio data.

b. Rankings of tennis players.

This is ordinal data, since you can rank order the players, but there is no clear numerical meaning to the order (for example, how much better is player 19 than player 20? – since we can’t answer that, it’s ordinal).

c. Weights of air conditioners.

Weight is a ratio level type of data. There is a defined 0 point (no weight), so ratios are meaningful – 50 pounds is twice as much as 25 pounds. Since there is an ordering, and ratios are meaningful, this is ratio data.

d. Temperatures inside 10 refrigerators.

Assuming the temperatures are in Fahrenheit, this is interval level data. The data does have a numerical meaning and ordering. In addition, the difference between 40 degrees and 41 degrees is well defined. However, in the F scale, the zero point doesn’t have a numerical meaning, so this cannot be ratio data. So 40 degrees isn’t “twice” as warm as 20 degrees.

e. Salaries of the top five CEOs in the United States.

Money is measured on the ratio scale, since there is a distinct 0 point – no money at all. In addition, you can set up meaningful ratios between various amounts of money.

f. Ratings of eight local plays (poor, fair, good, excellent).

This is ordinal data, since there is a clear ordering of the ranks, but there is no numerical meaning to them.

g. Times required for mechanics to do a tune-up.

Time is ratio data, since there is an ordering to amounts of time. In addition, the intervals of time are meaningful (seconds, minutes, etc). Finally, there is a zero point, which makes it ratio. For example, 1 hour is twice as long as 30 minutes.

h. Ages of students in a classroom.

Age is ratio data, since there is an ordering to years of age. In addition, the intervals of age are meaningful (years). Finally, there is a zero point, which makes it ratio. For example, someone who is 30 years old is twice as old as a 15 year old.

i. Marital status of patients in a physician’s office.

This is nominal data, since you cannot “rank order” the marital status. No one category is “better” than any other, and there is no numerical meaning.

j. Horsepower of tractor engines.

This is ratio data. There is a clear numeric meaning to the horsepower, and if an engine has 100 horsepower, that is truly twice as powerful as a 50 hp engine. Since ratios are meaningful, this is ratio data.

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Portion 3:

Describe what must be done to correct the graph in 200 - 250 words

This graph that compares internet speeds has many issues, but there are several easy things to do to it that could make it more reliable, understandable, and clear. Firstly, the Y axis should be labeled, with both a scale and also the units of measurement. This will allow us to confirm that the bars are all the proper heights and that there hasn’t been any distortion (there is no distortion… the 512 bar is indeed exactly four times higher than the 128 bar like you’d expect, but it took effort to come to that conclusion, while a Y axis labeling scheme would make it much simpler). The title of the graph should be changed to something like “Connection Speed for Various Internet Service Options”, so that we knew the connection speed was being compared, instead of something like the number of users in thousands. The graph could use a reference or some other type of link to a source, or where this data came from. That would help reassure the viewer that it isn’t made up. In addition, the green color of the “Cable” bar tends to make it look friendlier, especially compared to the yellow. The bars should all be the same color.

Table 1.1

(Hint) Problems Associated with the Graph

A misleading graph can lead to misrepresentation of data and a false conclusion such as the graph shown in Table 1.1. The graph does not include a source to check reliability, doesn’t have any numbers on the Y axis and is missing labels or units on the axes to represent the ranking of each factor of the data. There isn’t a way to decide what the difference of the 14.4 standard dial-up bar versus the 512 cable bar means on the graph. The numbers do not show any special meaning or indicate clearly what the data represents to enable the reader to analyze and interpret. Another problem is the exaggerated increase between the 14.4 bar or the 128 bar to the 512 bar, causing a one-dimensional comparison to be shown in two dimensions. The large difference between the dimensions gives a false visual representation, as to persuade the reader to make a false conclusion.

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