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Descriptive Statistics for Symmetrical and Skewed

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1. For each of the following, note whether the distribution is symmetrical, negatively skewed, or positively skewed.
a. Mean = 14, mode = 25, median = 19
b. Mean = 50, mode = 50, median = 50
c. Mean = 225.8, mode = 184, median = 199

2. A math test was given with the following results:
80, 69, 92, 75, 88, 37, 98, 92, 90, 81, 32, 50, 59, 66, 67, 66
Find the standard deviation, and variance for the scores.

3. For a particular sample of 50 scores on a psychology exam, the following results were obtained.

Mean = 78 Mode = 84 Median = 80 Standard deviation = 11
a. What score was earned by more students than any other score? Why?
b. What is the variance?

4. A student scored 70 percent on a test, and was in the 80th percentile. Explain these two numbers.

5. If the variance for reaction times for older dogs is 2.7 and the variance for reaction times for younger dogs is 1.3, please note the standard deviations for each age group. Using this information, what can you say about the variability of reaction times?

6. Collect data consisting of at least 20 values. (You may also create a data set with reasonable values for your variable).
a. Define the variable
b. Find the mean, median, mode, variance, and standard deviation for your data.
c. State which measurement of central tendency best describes the average and why.

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This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.

Solution provided by:
  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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