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Data Set Spread and Standard Deviation Calculations

Learn how to analyze data set spread using the range and compute standard deviation to measure data distribution. Follow examples to master the calculations.

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Data Set Spread and Standard Deviation Calculations

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  1. Section 14.3 Measures of Disbursement

  2. Objective • Determine the spread of a data set.

  3. Key Terms: • Range: the difference between the largest and the smallest data values in the set. • Standard Deviation: a measure based on calculating the distance of each data value from the mean.

  4. Computing the Standard Deviation • To compute the standard deviation for a sample consisting of n data values, do the following: • Find Χ • Compute Deviation: (X – Χ) • Compute (Deviation)2 • Compute s

  5. Computing the Sample Standard Deviation for a Frequency Distribution • To compute the sample standard deviation for a frequency distribution consisting of n data values, do the following: • Find Χ • Compute Deviation: (X – Χ) • Compute (Deviation)2 … Σcolumns 2, 3, and 6. • Compute s

  6. Example 1: • Find the range, mean, and standard deviation for the following data set. • TB pg. 814/1

  7. Example 2: • TB pg. 814/5

  8. Example 3:Calculate s for a frequency distribution. • TB pg. 814/ 11

  9. Example 4:Calculate s for a frequency distribution. • TB pg. 814/15

  10. Example 5:Find the mean and standard deviation. • TB pg. 815/19

  11. Example 6:Find the mean and standard deviation. • TB pg. 816/21

  12. Key Concept: • Calculate number of s from x. • Formula:

  13. Example 7:Calculate number of standard deviation from mean. • TB pg. 816/27

  14. Example 8:Calculate number of standard deviation from mean. • TB pg. 817/29

  15. Key Concept: • Calculating coefficient variable. • CV =

  16. Example 9:Calculate coefficient variable. • TB pg. 817/31

  17. Example 10:Calculate coefficient variable. • TB pg. 817/33

  18. Example 11:Calculate coefficient variable. • TB pg. 817/37

  19. Section 14.3 Assignment • Class work: • TB pg. 814/2 – 22 Even, and 28 – 38 Even • Please remember to write problems and show work. • This assignment is due Mon., 12/19/11. • THIS ASSIGNMENT WILL NOT BE ACCEPTED LATE!!!

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