1. Business 205

2. Review of last class NOIR Validity Reliability

3. Preview for Today Frequency, Range, Means, Medians, Modes Graphs Variance Standard Deviation

4. Descriptive Statistics A way to present quantitative descriptions in a manageable (aka: numerical) way Example: 52% Females, 48% Males

5. Qualitative Data Used to describe sample Class Frequency How many times it occurs in a given class Exec Board = Division Head = Staff = NameStatusScore DuckyExec Board100 WebbieExec Board95 MortimerExec Board95 WPDivision Head95 Baby DuckStaff8 PeepersStaff75

6. Qualitative Data Used to describe sample Class Relative Frequency Class frequency divided by total number in sample Staff = 2/6 =.33 Exec Board = Division Head = NameStatusScore DuckyExec Board100 WebbieExec Board95 MortimerExec Board95 WPDivision Head95 Baby DuckStaff8 PeepersStaff75

7. Qualitative Data Used to describe sample Class Percentage Multiply class relative frequency by 100. Staff =.33*100 = 33% Exec Board = Division Head = NameStatusScore DuckyExec Board100 WebbieExec Board95 MortimerExec Board95 WPDivision Head95 Baby DuckStaff8 PeepersStaff75

8. A Bunch of Scores… Sample Size (n) = 9 People/SampleScore 11 24 34 46 58 64 73 85 95

9. Distributions An arrangement of scores in order of magnitude Scores: 1, 4, 4, 6, 8, 3, 4, 5, 2 Distribution: 1, 2, 3, 4, 4, 4, 5, 6, 8

10. Frequency Distributions Listing of scores in magnitude with amount of people who received that score Scores: 1, 4, 4, 6, 8, 3, 4, 5, 2 Distribution: 1, 2, 3, 4, 4, 4, 5, 6, 8

11. Frequency Distributions NOTE: The total (f) MUST be equal to the sample size! In this example we had n = 9 so our f = 9!!! Score (X)Frequency (f) 11 21 31 43 51 61 81

12. Smart Frequency Distributions Colorf Pink Yellow White Green Purple Orange Unknown Total #: ______________ Colorf Pink Yellow White Green Purple Orange Unknown Total #: ______________

13. Graphs Bar Graphs Pie Charts Dot Plots Stem-and-Leaf Plots Histograms

14. Graphs Bar Chart Pie Chart Stem-and-Leaf 10 0 9 5 5 5 8 0 7 5 6 5 4 3 2 1

15. Try it out Create the following: Histogram Pie chart Stem-and-leaf plot PersonScore A98 B92 C25 D10 E81 F36 G

16. Central Tendency Information concerning the average or typical score of the sample interested in. **Do NOT confuse this with the mean…

17. Mean Arithmetic average of all scores 1. Sum (  ) the scores (X). 2. Divide by the sample size (n).

18. Mean Example Scores: 1, 4, 4, 6, 8, 3, 4, 5, 2 Distribution: 1, 2, 3, 4, 4, 4, 5, 6, 8 M = (1, 2, 3, 4, 4, 4, 5, 6, 8)/9 = 37/9 = 4.1111111

19. Median The midpoint of all the scores 1. Put all scores in order 2. Find the middle score 1. Interpolate score if necessary

20. Median Example, Non interpolated Scores: 1, 4, 4, 6, 8, 3, 4, 5, 2 Distribution: 1, 2, 3, 4, 4, 4, 5, 6, 8 1, 2, 3, 4, 4, 4, 5, 6, 8 Median = 4

21. Median Example, interpolated Scores: 1, 4, 4, 6, 8, 10, 3, 5, 5, 2 Distribution: 1, 2, 3, 4, 4, 5, 5, 6, 8, 10 1, 2, 3, 4, 4, 5, 5, 6, 8, 10 Median = (4+5)/2 = 9/2 =4.5 Median = 4.5

22. Mode The score that appears the most 1. Put the scores in order 2. Find the frequencies of the scores 3. Choose the one that appears the most times

23. Mode Example 4 appears 3 times. Mode = 4 Score (X)Frequency (f) 11 21 31 43 51 61 81

24. Mode Example What if they are all the same in frequency? Mode = ? Score (X)Frequency (f) 11 21 31 41 51 61 81

25. How did they compare? Mean = 4.11 Median = 4 Mode = 4 Can you have more than 1 mode? Can you have more than 1 mean? Can you have more than 1 median?

26. Normal Distribution Curve Mean = Median = Mode

27. Positively Skewed Mode Median Mean

28. Negatively Skewed Mean Median Mode

29. Skew this Distribution: 1, 2, 8, 9, 9 Mean = Median = Mode = Graph:

30. Range (R) Measurement of the width of scores. R = high score – low score + 1

31. Range Example Scores: 1, 4, 4, 6, 8, 3, 4, 5, 2 Distribution: 1, 2, 3, 4, 4, 4, 5, 6, 8 CORRECT: High Score = 8; Low Score = 1 R = 8 – 1 + 1 = 8 INCORRECT: High Score = 8; Low Score = 1 R = 8-1 = 7

32. Standard Deviation (SD) How much scores in a distribution differ from the mean. 1. Find the mean 2. Subtract each score from the mean (x) 3. Square each difference (x 2 ) and sum(  ) 4. Divide the sum by the sample size (n) 5. Take the square root of the number

33. Standard Deviation Example Mean = 4.11  x 2 = 34.89 =  [(34.89)/9] = 1.97 Scores (X)X – Meanxx2x2 11 – 4.11-3.119.6721 22 – 4.11-2.114.4521 33 – 4.11-1.111.2321 44 – 4.11-.11.0121 44 – 4.11-.11.0121 44 – 4.11-.11.0121 55 – 4.11.89.7921 66 – 4.111.893.5721 88 – 4.113.8915.132

34. Standard Deviation Shortcut For Example Mean = 4.11  X 2 = (1+4+9+16+16+16+25+ 36+64) = 187 SD =  [(187/9)-(4.11 2) ] = 1.97 Scores (X)X2X2 11 24 39 416 4 4 525 636 864

35. Variance How much all the scores in the distribution vary from the mean. V = SD 2

36. In Class Example: Range You have the following scores: 8, 10, 4, 4 R = high score – low score + 1

37. In Class Example: Distribution You have the following scores: 8, 10, 4, 4 Score (X)Frequency (f)

38. In Class Example: Mean, Median, Mode You have the following scores: 8, 10, 4, 4 Mean Median Mode

39. In Class Example: Standard Deviation You have the following scores: 8, 10, 4, 4 Scores (X) X – Meanxx2x2 4 4 8 10

40. In Class Example: Standard Deviation You have the following scores: 8, 10, 4, 4

41. In Class Example: Variance You have the following scores: 8, 10, 4, 4