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General Questions about Descriptive Statistics

1. Compare and contrast the advantages and/or disadvantages of using a bar chart, a pie chart, or a Pareto diagram.

2. Discuss the differences among the mean, median, and mode. What are the advantages and disadvantages of each?

3. Explain how the empirical rule helps explain the ways in which the values in a set of numerical data cluster and distribute.

4. Regarding probability, discuss the differences between mutually exclusive events and collectively exhaustive events.

5. Explain the ways in which conditional probability relate to the concept of statistical independence.

6. Identify the distinguishing properties of a normal distribution. Please answer in detail.

Solution Preview

1. A bar chart shows you the mean (average) scores of several groups. It is good to use when you have categorical variables (e.g. when you're comparing men and women or when you're comparing three breeds of dogs on a learning task), but is inappropriate for continuous data (e.g. if you were comparing performance on a learning task over 10 days).

A pie chart has very few advantages. It is also used for categorical data and provides the proportion of scores that fell in each category, but it is much harder to read than a bar chart. If you want to talk about proportions, you're much better to use a histogram (which basically looks like a bar chart but plots proportions of scores instead of group means) than a pie chart. If the differences in proportions are really big, a pie chart can point out the most common score, but often it's just really hard to tell the difference in size between the pie 'slices'.

A Pareto diagram also shows the frequency of scores for categorical data, or can be used to show mean scores for categorical data. It presents information in bar and line form. It orders the bars from most frequent category (at the left) to least frequent category (at the right), so it's easy to tell which category was the most 'important'. The line indicates the cumulative frequency of scores, so you can tell what proportion of total scores has occurred for the categories (e.g. you ...

Solution Summary

This solution discusses descriptive statistics.

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