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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.

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3.1 Averages and Variation

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  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

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