1. 1 Chapter 2 Bivariate Data A set of data that contains information on two variables. Multivariate A set of data that contains information on more than two variables.

2. 2 Qwertry Keyboard Word Ratings Table 2-1 2251263342 40577566810 72210582542 6261727238 15252142263 17

3. 3 Figure 2-6 Dot Plot

4. 4 Boxplots 5 - number summary  Minimum  first quartile Q 1  Median (Q 2 )  third quartile Q 3  Maximum Min Med Q3Q3 Q1Q1 Max

5. 5 Boxplots ( Box-and-Whisker Diagram) Reveals the:  center of the data  spread of the data  distribution of the data  presence of outliers Excellent for comparing two or more data sets

6. 6 Outliers  a value located very far away from almost all of the other values  an extreme value  can have a dramatic effect on the mean, standard deviation, and on the scale of the histogram so that the true nature of the distribution is totally obscured

7. 7 Boxplots Min Q1Q1 Q2Q2 Q3Q3 Max

8. 8 Qwertry Keyboard Word Ratings Table 2-1 2251263342 40577566810 72210582542 6261727238 15252142263 17

9. 9 Boxplots Boxplot of Qwerty Word Ratings 2 46 8101214 0 2 46 0

10. 10 Interquartile Range Median (Q2) X maximum X minimum Q1Q3 Example: 25% 25% 12 30 45 57 70 Interquartile range = 57 – 30 = 27

11. 11 Bell-Shaped Boxplots

12. 12 Bell-ShapedSkewed Boxplots Uniform

13. 13 Shape of a Distribution Describes how data is distributed Shape - Symmetric or skewed Mean = Median Mean < Median Median < Mean Right-Skewed Left-SkewedSymmetric

14. 14 Outliers Possible Outlier, or unusual score, is a score between the inner and outer fences. Probable Outlier, or rare score, is a score beyond the outer fence

15. 15 Q1Q1 Q3Q3 1.5(IQR) Outer Fences Inner Fences Possible Outliers Probable Outliers

16. 16 Regions for Mild and Extreme Outliers in a Box Plot

17. 17 2 46 14 IQR = 4 1.5*4 = 6 0 12-4 18 -10 Inner Fence Outer Fence 14 is a possible outlier or unusual score No probable or rare scores 0 and 10 are the adjacent scores

18. 18 Confidence Interval for a median An interval constructed in a specific manner, in which the true median can be expected to lie in a certain percentage of the time. True Median The median of the larger group, or population, from which the sample was taken. Adjacent Score The score on each side of the median that come closest but do not reach the inner fences

19. 19 The constant 1.57 is a factor that results in a notch centered about the median such that 95% of the time medians whose differences are due to chance results in overlapping notches. NOTCHED BOX PLOTS

20. 20

21. 21

22. 22 CONCLUSION: The two groups from which these samples were taken have different median cholesterol counts

23. 23 Construct two notched box plots to determine whether Or not the difference in medians is statistically significant At the 95 % confidence level.

24. 24 3.19 2.83 3.49 1.94 3.77 2.96 2.42 3.17 2.05 3.90 Humanities Mathematics IQR = 3.49 – 2.83 =.65IQR = 3.17 – 2.42 =.75 Notch width =.20 Notch width =.19

25. 25 1.94 2.83 3.19 3.49 3.77 3.09 3.29 2.05 2.42 2.96 3.17 3.90 2.86 3.06 Since the notches do not overlap, there is evidence At the 95% level that the difference in medians is significant