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 111 14 11 14 15 17 18 19 20 Ex 24 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 4256 = 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 XMedian 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 82.5041 Midterm 92.1513.8 Final 72.2014.4 Lab 98.109.8 HW 100.055 ∑w = ∑xw =

14. Weighted Mean Source Score x Weight w xw Test 82.5041 Midterm 92.1513.8 Final 72.2014.4 Lab 98.109.8 HW 100.055 ∑w = 1.00 ∑xw = 84

15. Warm Up FrequencyMajorSalary 10Math68000 Science72000 51History40000 Find the weighted mean

16. Warm Up FrequencyMajorSalary 24Math68000 31Science72000 51History40000 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 AgeFMidpoint (x)xf 0-82 9-1715 18-2612 27-356 ∑∫= ∑x∫=

21. Grouped Data Example AgeFMidpoint (x)xf 0-824 9-171513 18-261222 27-35631 ∑∫= ∑x∫=

22. Grouped Data Example AgeFMidpoint (x)xf 0-8248 9-171513195 18-261222264 27-35631186 ∑∫= ∑x∫=

23. Grouped Data Example AgeFMidpoint (x)xf 0-8248 9-171513195 18-261222264 27-35631186 ∑∫= 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. 1.Symmetric 2.Uniform 3.Skewed Left 4.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 ClassUnit/CreditGradeTotal

30. Example 1 B in one 3 unit class D in one 5 unit class ClassUnit/CreditGradeTotal 1339 1515

31. Example 1 B in one 3 unit class D in one 5 unit class ClassUnit/CreditGradeTotal 1339 1515 ∑unit= ∑total=

32. Example 1 B in one 3 unit class D in one 5 unit class ClassUnit/CreditGradeTotal 1339 1515 ∑unit=8 ∑total=14

33. Example 1 ClassUnit/CreditGradeTotal 1339 1515 ∑unit=8 ∑total=14 ∑total =14 = 1.75 GPA ∑unit8