1. STAT 110 - Section 5 Lecture 15 Professor Hao Wang University of South Carolina Spring 2012 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

2. Last time: Histogram Example: Mid-term grades

3. When describing a data set, the three keys are: 1.Shape 2.Center 3.Spread The histogram is one of the tools to help us with the shape.

4. symmetric – the right and left sides of the histogram are approximately mirror images of each other

5. Symmetric example: Human IQ

6. Symmetric example: Human Height

7. skewed left – the left side of the histogram (the half containing the smaller values) extends much farther than the right

8. skewed left example: our mid-term grades

9. skewed left example: stock returns

10. skewed right – the right side of the histogram (the half with the larger values) extends much farther than the left

11. skewed right example: income

12. skewed right example: BMI

13. unimodal – the histogram has one major spike or tall area, and the values tend to get smaller on either side of it; bimodal would be two major spikes or tall areas

14. Bimodal example: old faith geyser duration of eruption

15. The graph to the right is: A)Skewed Right B)Skewed Left C) Symmetric D) Bimodal E) Two of the Above

16. The graph to the right is: A)Skewed Right B)Skewed Left C) Symmetric D) Bimodal E) Two of the Above

17. The graph to the right is: A)Skewed Right B)Skewed Left C) Symmetric D) Bimodal E) Two of the Above

18. Stemplots Test score data: 88, 90, 62, 76, 84, 89, 92, 73, 55, 76, 88, 47, 77, 93 Stemplot of Test Score Data How would you describe the distribution? 456789456789 7 5 2 3 6 6 7 4 8 8 9 0 2 3

19. Stemplots When you have small data sets, stemplots are a good way to display the data. Advantages over Histograms: 1. quicker to make 2. presents more detailed information

20. Stemplots To make a stemplot: 1. Separate each observation into a stem and a leaf. 2. Write the stems in a vertical column with the smallest at the top. 3. Draw a vertical line at the right of this column. 4. Write each leaf in the row to the right of its stem, in increasing order out from the stem.

21. Stemplots So, what’s a stem and what’s a leaf? A stem consists of all but the final (rightmost) digit. A leaf is the final digit. Stems may have as many digits as needed. Each leaf contains only a single digit.

22. Stemplots Back to our test score data set… 88, 90, 62, 76, 84, 89, 92, 73, 55, 76, 88, 47, 77, 93 1.Separate into stem and leaf. stem – 8, 9, 6, 7, 8, 8, 9, 7, 5, 7, 8, 4, 7, 9 leaf – 8, 0, 2, 6, 4, 9, 2, 3, 5, 6, 8, 7, 7, 3 2.Write stems in vertical column – 4, 5, 6, 7, 8, 9 3.Draw the vertical line. 4.Write each leaf.

23. Stemplots Stemplot of Test Score Data How would you describe the distribution? 4 5 6 7 8 9 7 5 2 3 6 6 7 4 8 8 9 0 2 3

24. 4 5 6 7 8 9 7 5 2 3 6 6 7 4 8 8 9 0 2 3 The smallest observation in this stemplot is A)09 B)39 C)47 D)74 E)93

25. 4 5 6 7 8 9 7 5 2 3 6 6 7 4 8 8 9 0 2 3 This data set is A)Skewed Left B)Symmetric C)Skewed Right