1 / 15

Chapter 3 : Averages and Variation

Chapter 3 : Averages and Variation. Section 2 : Measures of Dispersion. Reflects the amount of spread or variability in a collection of data. Example : Find the mean and median for the following sets of data. 71 73 74 76 77 79 Mean & Median = 75 46 63 70 80 91 100

rbrousseau
Download Presentation

Chapter 3 : Averages and Variation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chapter 3: Averages and Variation Section 2: Measures of Dispersion

  2. Reflects the amount of spread or variability in a collection of data. Example: Find the mean and median for the following sets of data. 71 73 74 76 77 79 Mean & Median = 75 46 63 70 80 91 100 Mean & Median = 75 Measure of Dispersion

  3. A measure of central tendency is incapable of detecting differences in the spread or variability in a collection of data values.

  4. Range • The difference between the highest and lowest data values. • Range = Highest – Lowest

  5. 1 2 3 4 5 6 7 8 9 10 11 Example: Find the mean and range for the following sets of data. Number of Books Read by History Students Mean = 6 Range = 10

  6. 1 2 3 4 5 6 7 8 9 10 11 Number of Books Read by Sociology Student Mean = 6 Range = 10

  7. A A A B B B X X 38 25 34 24 26 23 24 22 20 21 20 19 16 18 14 17 6 16 2 15 The sum of the deviations from the mean always equals zero.

  8. Variance • The average of the sum of the squared deviation scores. • Population Variance = • Sample Variance s2 =

  9. Standard Deviation • Square root of the variance • Typical distance from the mean for the data values • Population Standard Deviation = • Sample Standard Deviation s=

  10. Example • Find the population variance for the following data values. • 6 11 5 1 6 6 7 5 7 6 ***First find the population mean =

  11. Population Variance Sample (cont) x x – (x – )2 6 0 0 11 5 25 5 -1 1 1 -5 25 6 0 0 6 0 0 7 1 1 5 -1 1 7 1 1 6 0 0 54

  12. Population Variance Sample (cont) • = = = 5.4 • Using the previous example, the population standard deviation would be found by: = = 2.32

  13. Example Sample Variance • Find the sample variance and sample standard deviation for the following data values. 4 3 7 4 2 • First find the sample mean = = = 4

  14. Sample Variance Example (Cont) Use a table to calculate the sample variance. x x – (x – )2 2 -2 4 4 0 0 3 -1 1 7 3 9 4 0 0 14

  15. Sample Variance Example (Cont) • s2 = = = 3.5 • s = = 1.87 Take the square root of the sample variance to find the sample standard deviation.

More Related