1 / 21

3.1 Averages and Variation

3.1 Averages and Variation. February 7, 2012. Three types of “average”: mean, median, and mode. Mode: the value that occurs most frequently. Find the mode:. 6, 7, 2, 3, 4, 6, 2, 6. Find the mode:. 6, 7, 2, 3, 4, 5, 9, 8 There is no mode for this data. The Median.

cricket
Download Presentation

3.1 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. 3.1Averages and Variation February 7, 2012

  2. Three types of “average”:mean, median, and mode

  3. Mode: the value that occurs most frequently Find the mode: • 6, 7, 2, 3, 4, 6, 2, 6

  4. Find the mode: 6, 7, 2, 3, 4, 5, 9, 8 There is no mode for this data.

  5. The Median the central value of an ordered distribution

  6. To find the median of raw data: • Oorder the data from smallest to largest. • Ffor an odd number of data values, the median is the middle value. • Ffor an even number of data values, the median is found by dividing the sum of the two middle values by two.

  7. Find the median: Data:5, 2, 7, 1, 4, 3, 2 Rearrange:1, 2, 2, 3, 4, 5, 7 The median is 3.

  8. Find the median: Data: 31, 57, 12, 22, 43, 50 Rearrange: 12, 22, 31, 43, 50, 57 The median is the average of the middle two values =

  9. The Mean • The mean of a collection of data is found by: • ssumming all the entries • ddividing by the number of entries

  10. Find the mean: 6, 7, 2, 3, 4, 5, 2, 8

  11. Sigma Notation • Tthe symbol  means “sum the following.” • is the Greek letter (capital) sigma.

  12. Notations for mean Sample mean “x bar” Population mean Greek letter (mu)

  13. Number of entries in a set of data • Iif the data represents a sample, the number of entries = n. • Iif the data represents an entire population, the number of entries = N.

  14. Sample mean

  15. Population mean

  16. Resistant Measure a measure that is not influenced by extremely high or low data values

  17. Which is less resistant? • Mmean • Mmedian The mean is less resistant. It can be made arbitrarily large by increasing the size of one value.

  18. Trimmed Mean a measure of center that is more resistant than the mean but is still sensitive to specific data values

  19. To calculate a (5 or 10%) trimmed mean • Oorder the data from smallest to largest. • Ddelete the bottom 5 or 10% of the data. • Ddelete the same percent from the top of the data. • Ccompute the mean of the remaining 80 or 90% of the data.

  20. Compute a 10% trimmed mean: 15, 17, 18, 20, 20, 25, 30, 32, 36, 60 • Ddelete the top and bottom 10% • Nnew data list: • 17, 18, 20, 20, 25, 30, 32, 36 • 110% trimmed mean =

  21. Pg. 96-98 2,4,8,11

More Related