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This course is designed to acquaint the student with the principles of descriptive and inferential statistics. Topics will include: types of data, frequency distributions and histograms, measures of central tendency, measures of variation, probability, probability distributions including binomial, normal probability and student's t distributions, standard scores, confidence intervals, hypothesis testing, correlation, and linear regression analysis. This course is open to any student interested in general statistics and it will include applications pertaining to students majoring in athletic training, pre-nursing and business.

1

After constructing a relative frequency distribution summarizing IQ scores of college students, what should be the sum of the relative frequencies?

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Weights of statistics students were obtained by a teacher as part of an experiment conducted for the class. The last digit of those weights are listed below. Construct a frequency distribution with 10 classes.

0 0 0 0 0 0 0 0 0 1 2 2 3 4 4 4 5 5 5 5 5 5 5 5 5 6 6 8 8 9 9

Based on the distribution, do the weights appear to be reported or actually measured?

What can be said about the accuracy of the results?

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Refer to the accompanying data set and use the 30 screw lengths to construct a frequency distribution. Begin with a lower class limit of 1.220 in, and use a class width of 0.010 in. The screws were labeled as having a length of 1 1/4 in.

Does the frequency distribution appear to be consistent with the label? Why or why not?

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Among fatal plane crashes that occurred during the past 65 years, 657 were due to pilot error, 71 were due to other human error, 613 were due to weather, 348 were due to mechanical problems, and 581 were due to sabotage.

What is the most serious threat to aviation safety, and can anything be done about it?

14

Class width is found by _______.

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The population of ages at inauguration of all U.S. Presidents who had professions in the military is 62, 46, 68, 64, 57.

Why does it not make sense to construct a histogram for this data set?

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The last digit of the heights of 56 statistics students were obtained as part of an experiment conducted for a class.

Use the frequency distribution to the right to construct a histogram.

What can be concluded from the distribution of the digits? Specifically, do the heights appear to be reported or actually measured?

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A bar chart and a Pareto chart both use bars to show frequencies of categories of categorical data. What characteristic distinguishes a Pareto chart from a bar chart, and how does that characteristic help us in understanding the data?

** In a Pareto chart, the bars are always arranged in
descending order according to frequencies. The Pareto chart helps us
understand data by drawing attention to the more important
categories, which have the highest frequencies.**

A bar chart uses bars of equal width to show frequencies of categorical data. The vertical scale represents frequencies or relative frequencies. The horizontal scale identifies the different categories of qualitative data. When one wants a bar chart to draw attention to the more important categories, one can use a Pareto chart, which is a bar chart for categorical data, with the added stipulation that the bars are arranged in descending order according to frequencies. The bars decrease in height from left to right.

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Construct a scatter diagram using the data table to the right. This data is from a study comparing the amount of tar and carbon monoxide (CO) in cigarettes. Use tar for the horizontal scale and use carbon monoxide (CO) for the vertical scale.

Determine whether there appears to be a relationship between cigarette tar and CO.

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**Yes, the population appears to have a normal distribution
because the dotplot resembles a "bell" shape.**

When graphed, a normal distribution has an approximate "bell" shape. In a normal distribution, (1) the frequencies increase to a maximum and then decrease, and (2) the graph has symmetry, with the left half of the graph being roughly a mirror image of the right half.

**Yes, the volume of 50 oz appears to be an outlier because it
is far away from the other volumes.**

Outliers are sample values that lie very far away from the vast majority of the other sample values.

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**No, the distribution is not dramatically far from being a
normal distribution with a "bell" shape, so there is not
strong evidence against a normal distribution.**

When plotted, a normal distribution has an approximate "bell" shape. In a normal distribution, the frequencies increase to a maximum and then decrease, and the distribution has symmetry, with the frequencies of the lower values being roughly a mirror image of the frequencies of the higher values.

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In a recent year, 4386 people were killed while working. Here is a breakdown of causes: combustibles (2329); substances (605); equipment (590); violence (465); transportation ( 204); falls (193).

Use the data to construct a Pareto chart. Compare the Pareto chart to the pie chart.

Which graph is more effective in showing the relative importance of the causes of work-related deaths?

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**The frequency polygon appears to roughly approximate a normal
distribution because the frequencies increase to a maximum, then
decrease, and the graph is roughly symmetric.**

When graphed, a normal distribution has an approximate "bell" shape. In a normal distribution, the frequencies increase to a maximum and then decrease, and the distribution has symmetry, with the frequencies of the lower values being roughly a mirror image of the frequencies of the higher values.

29

**The frequency polygon does not appear to approximate a normal
distribution because the frequencies do not increase to a maximum
and then decrease, and the graph is not symmetric.**

When graphed, a normal distribution has an approximate "bell" shape. In a normal distribution, the frequencies increase to a maximum and then decrease, and the distribution has symmetry, with the frequencies of the lower values being roughly a mirror image of the frequencies of the higher values.

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The graph to the right shows the braking distances for different cars measured under the same conditions.

Describe the ways in which this graph might be deceptive.

How much greater is the braking distance of Car A than the braking distance of Car C? Draw the graph in a way that depicts the data more fairly.

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Which of the following is NOT true about statistical graphs?

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Which of the following is a common distortion that occurs in graphs?

** Using a two-dimensional object to represent data that are
one-dimensional in nature**

Using a two-dimensional object to represent data that are one-dimensional in nature is a bad practice that distorts the meaning of the data. When drawing such objects, artists can create false impressions that distort differences.

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