1. Chapter 4 Displaying Quantitative Data

2. Quantitative variables Quantitative variables- record measurements or amounts of something. Must have units or a variable in which the numbers act as numerical values

3. Types of Displays Histogram Stem and Leaf Displays Dotplots

4. Histogram A histogram uses adjacent bars to show the distribution of values in a quantitative variable. Looks very similar to a bar graph but there are differences. The horizontal axis is continuous not just labeled.

5. An example The histogram shown below gives the number of children visited a particular zoo..

6. Histogram A histogram is more convenient than a dot-plot or a stem and leaf plot because you don't have to represent each data point. However, you don't get to see the value of each data point. So a table of data and summary statistics would help people interpret the data.

7. Be Careful A histogram gives the number of data points that fall into equal intervals. Care must be taken in choosing the intervals because it can affect the shape of the graph and misrepresent the true data.

8. 1 st graph The first graph is uses intervals of size 10 yielding the intervals 40-50, 50-60, etc. In this case, Yemen had a life expectancy of 50 and was placed in the 50-60 column. Usually, borderline values are placed in the higher column.

9. 2 nd Graph In the second graph, the intervals are 40- 45, 45-50, 50-55, etc. This affects the shape of the graph.

10. Stem and Leaf Displays Shows quantitative data values in a way that sketches the distribution of the data. The stem-and-leaf plot below shows the number of students enrolled in a dance class in the past 12 years. The number of students are 81, 84, 85, 86, 93, 94, 97, 100, 102, 103, 110, and 111.

11. Dotplot Graphs a dot for each case against a single axis Graph the following number 5, 5,5,5,5,5,5,10,10,10,10,10 etc

12. Dotplot with two sets of data Example

13. Shape To describe the shape of a distribution, look for Symmetry versus skewness Single versus multiple modes

14. Symmetrical A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other.

15. Symmetrical Symmetrical Histogram

16. Dotplot Dots are mirrored images

17. Stem and leaf Example

18. Skewed A distribution is skewed if it is not symmetric and one tail stretched out further than the other. Skewed left- when the longer tail stretches to the left. Skewed right-when the longer tail stretched to the right

19. Examples Skewed right

20. Skewed left Left

21. All three Examples

22. Funny example http://www.herkimershideaway.org/apstati stics/ymmsum99/ymm111.htm

23. Center A value that attempts the impossible by summarizing the entire distribution with a single number, a “typical” value

24. Spread A numerical summary of how tightly the values are clustered around the center

25. Mode

26. Unimodal

27. Uniform

28. Symmetrical

29. Tails

30. Outloiers

31. Timeplots

32. Skewness To the right

33. Skewness To the left