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Descriptive Statistics

Descriptive Statistics. What a Data Set Tells Us. Measures of Dispersion. 14.3. Compute the range of a data set. Understand how the standard deviation measures the spread of a distribution. Use the coefficient of variation to compare the standard deviations of different distributions.

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Descriptive Statistics

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  1. Descriptive Statistics What a Data Set Tells Us

  2. Measures of Dispersion 14.3 • Compute the range of a data set. • Understand how the standard deviation measures the spread of a distribution. • Use the coefficient of variation to compare the standard deviations of different distributions.

  3. The Range of a Data Set

  4. The Range of a Data Set • Example: Find the range of the heights of the people listed in the accompanying table. • Solution:

  5. Standard Deviation

  6. Standard Deviation

  7. Standard Deviation

  8. Standard Deviation • Example: A company has hired six interns. After 4 months, their work records show the following number of work days missed for each worker: • 0, 2, 1, 4, 2, 3 • Find the standard deviation of this data set. • Solution: • Mean: (continued on next slide)

  9. Standard Deviation • We calculate the squares of the deviations of the data values from the mean. • Standard Deviation:

  10. Standard Deviation

  11. Standard Deviation • Example: The following are the closing prices for a stock for the past 20 trading sessions: • 37, 39, 39, 40, 40, 38, 38, 39, 40, 41, • 41, 39, 41, 42, 42, 44, 39, 40, 40, 41 • What is the standard deviation for this data set? • Solution: • Mean: (sum of the closing prices is 800) (continued on next slide)

  12. Standard Deviation • We create a table with values that will facilitate computing the standard deviation. • Standard Deviation:

  13. Standard Deviation Comparing Standard Deviations All three distributions have a mean and median of 5; however, as the spread of the distribution increases, so does the standard deviation.

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