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Notes 2.3

Notes 2.3. Measures of Central Tendency. Central Tendency. A measure of central tendency is a value that represents a typical or central entry of a data set. The most common ones are mean, median and mode.

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Notes 2.3

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  1. Notes 2.3 Measures of Central Tendency

  2. Central Tendency • A measure of central tendency is a value that represents a typical or central entry of a data set. The most common ones are mean, median and mode. • Mean: the sum of all the entries, then divided by the number of entries in the data set

  3. Find the mean • 12, 18, 19, 2, 18, 31, 24, 30, 9, 11, 14, 16, 18

  4. Median: is the middle data entry when the data is sorted is ascending (from smallest to greatest) or descending (from greatest to smallest) order. • Find the median • 8 9 11 1 14 2 15 17 18 19 31 24 9

  5. Mode: the entry with the greatest frequency. If no entry is repeated the data set has no mode. If two numbers have the same amount of frequency both numbers are the mode. • Ex 1 11 14 11 14 15 17 18 19 20 • Ex 2 4 8 9 14 15 8 19 21 7 31

  6. Warm Up Find the mean, median and mode. Number of time someone has gone fishing. 1 0 4 0 5 0 34 0 1 0 2 4 0 0 0 0 2 1 0

  7. Notes 2.3 Part 2 Weighted Mean

  8. Outlier • An outlier is a data entry that is far removed from the other data entries. • Do the following data sets have an outlier. • 1) 4 5 8 4 5 7 1 4 34 5 7 8 5 • 2) 1 2 3 4 4 3 2 5 1 3 5 4 3 4 2

  9. Which measure of central tendency best describes a typical data entry? • It all depends on whether the data entries have a outlier. • If the data set has an outlier the median is best • If a data set does not have an outlier the mean is best. • The mode is almost never the best to describe a data set.

  10. The mean is heavily influenced by an outlier that is why it is not the best method to describe a data set. 4 2 3 5 42 56 = 11.2 5 Mean is 11.2 • The median is not influenced by an outlier therefore when an outlier is present, it is the best method to describe 4 2 3 5 42 2 3 4 5 42 X X X X Median is 4

  11. Weighted mean • Weighted mean: is the mean of a data set whose entries have varying weights. A weighted mean is given by

  12. Weighted Mean Source Score x Weight w     xw  Test 82 .50 Midterm 92 .15 Final 72 .20 Lab 98 .10 HW 100 .05 ∑w = ∑xw =

  13. Weighted Mean Source Score x Weight w   xw  Test 82 .50 41 Midterm 92 .15 13.8 Final 72 .20 14.4 Lab 98 .10 9.8 HW 100 .05 5 ∑w = ∑xw =

  14. Weighted Mean Source Score x Weight w   xw  Test 82 .50 41 Midterm 92 .15 13.8 Final 72 .20 14.4 Lab 98 .10 9.8 HW 100 .05 5 ∑w = 1.00 ∑xw = 84

  15. Warm Up Frequency Major Salary 10 Math 68000 Science 72000 51 History 40000 Find the weighted mean

  16. Warm Up Frequency Major Salary 24 Math 68000 31 Science 72000 51 History 40000 Find the weighted mean

  17. Notes 2.3 (Part 3) Grouped Data

  18. Grouped Data Equation Useful for when there are a lot of data entries. 2 4 9 10 10 10 11 11 12 13 14 15 17 17 17 17 17 18 18 18 18 19 19 20 21 21 21 24 25 27 28 28 28 29 31

  19. Grouped Data Mean Equation

  20. Grouped Data Example Age F Midpoint (x) xf 0-8 2 9-17 15 18-26 12 27-35 6 ∑∫= ∑x∫=

  21. Grouped Data Example Age F Midpoint (x) xf 0-8 2 4 9-17 15 13 18-26 12 22 27-35 6 31 ∑∫= ∑x∫=

  22. Grouped Data Example Age F Midpoint (x) xf 0-8 2 4 8 9-17 15 13 195 18-26 12 22 264 27-35 6 31 186 ∑∫= ∑x∫=

  23. Grouped Data Example Age F Midpoint (x) xf 0-8 2 4 8 9-17 15 13 195 18-26 12 22 264 27-35 6 31 186 ∑∫= 35 ∑x∫= 653

  24. Example #1 ∑x∫ = 625 = 18.66 ∑∫ 35

  25. Notes 2.3 (Part 4) Finding GPA

  26. Shapes of Distribution Go to page 63 and copy the four shapes of distribution. Make sure to copy the shape of the graph. • Symmetric • Uniform • Skewed Left • Skewed Right

  27. How to find your GPA All classes are not created equal in colleges and universities. Some are worth 1 credit, 2 credit, 3 credits and some are even worth 6 to 7 credits. Lets calculate a sample GPA

  28. Example 1 B in one 3 unit class D in one 5 unit class

  29. Example 1 B in one 3 unit class D in one 5 unit class Class Unit/Credit Grade Total

  30. Example 1 B in one 3 unit class D in one 5 unit class Class Unit/Credit Grade Total 1 3 3 9 1 5 1 5

  31. Example 1 B in one 3 unit class D in one 5 unit class Class Unit/Credit Grade Total 1 3 3 9 1 5 1 5 ∑unit= ∑total=

  32. Example 1 B in one 3 unit class D in one 5 unit class Class Unit/Credit Grade Total 1 3 3 9 1 5 1 5 ∑unit= 8 ∑total=14

  33. Example 1 Class Unit/Credit Grade Total 1 3 3 9 1 5 1 5 ∑unit= 8 ∑total=14 ∑total = 14 = 1.75 GPA ∑unit 8

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