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Understanding Measures of Dispersion: Range and Standard Deviation in Data Analysis

This resource explores the essential concepts of measures of dispersion, focusing on the range and standard deviation of data sets. Learn how to compute the range, understand the significance of standard deviation in assessing the spread of distributions, and use the coefficient of variation for comparing different datasets. Through practical examples, including intern workdays and stock prices, we illustrate how to calculate these metrics and their implications for data analysis. Gain a deeper understanding of how dispersion impacts data interpretation.

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Understanding Measures of Dispersion: Range and Standard Deviation in Data Analysis

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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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