Exercises - Descriptive Statistics

1. Given the following data: 100, 95, 95, 90, 85, 75, 65, 60, 55. Find the median, mean, and mode. Is there a most appropriate measure?

2. Make a sketch of the following, indicating the approximate locations for the mean, median and mode:

1. a normal distribution
2. a skewed distribution
3. a rectangular distribution
3. Given the data set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ''x''. Find the smallest positive integer value for ''x'' such that ''x'' is an outlier. Find the value for ''both'' definitions.

4. Given the following set of golf scores: 67, 70, 72, 74, 76, 76, 78, 80, 82, 85. Find the median, mean, mode, and standard deviation. What percentage of scores are in the interval of one standard deviation from the mean?

5. Give at least five uses and at least five misuses of statistics. Use complete sentences and elaborate as needed for clarity.

6. Give the four levels or categories of data and give an example of each.

7. What amount of data does Chebyshev's Theorem guarantee is within three standard deviations from the mean? Compare this result to the empirical rule. Why are there differences?

8. Given the following grades on a test: 86, 92, 100, 93, 89, 95, 79, 98, 68, 62, 71, 75, 88, 86, 93, 81, 100, 86, 96, 52

1. Make a stem-and-leaf plot to represent this data.
2. Find the mode, median, mean, range, standard deviation, and interquartile range
3. What percentage of scores lie within one standard deviation from the mean? two standard deviations?
4. Are there any outliers? Explain clearly.
9. What is an experimental design and why is it important? Describe a completely randomized experimental design and a rigorously controlled design.

10. Given the following sample of freshman GPA scores:

$$2.2, 2.9, 3.5, 4.0, 3.9, 3.5, 2.9, 2.8, 3.1, 3.5, 3.8, 4.0, 3.8, 2.4, 3.9, 3.4, 2.8, 2.4, 1.8, 3.6, 3.1, 2.9, 3.8, 4.0$$
1. Is there an outlier? (Check both tests and explain)
2. Draw a frequency histogram using 5 to 6 categories. Be consistent with the rules for making histograms.
3. Is the distribution significantly skewed?
4. What percentage of scores is within one standard deviation of the mean? two standard deviations? three standard deviations?
5. Are your findings consistent with the minimum amount of data within two standard deviations guaranteed by Chebyshev's Theorem?