2. Types of variables

3. Categorical variables
or qualitative
identifies basic differentiating characteristics of the population

4. Numerical variables or quantitative
observations or measurements take on numerical values
makes sense to average these values
two types - discrete & continuous

5. Discrete (numerical)
listable set of values
usually counts of items

6. Continuous (numerical)
data can take on any values in the domain of the variable
usually measurements of something

7. Classification by the number of variables
Univariate - data that describes a single characteristic of the population
Bivariate - data that describes two characteristics of the population
Multivariate - data that describes more than two characteristics (beyond the scope of this course

8. Graphs for categorical data

9. Bar Graph Used for categorical data Bars do not touch
Categorical variable is typically on the horizontal axis
To describe – comment on which occurred the most often or least often
May make a double bar graph or segmented bar graph for bivariate categorical data sets

10. Using class survey data: graph birth month graph gender & handedness

11. Pie (Circle) graph Used for categorical data To make:
Proportion °
Using a protractor, mark off each part
To describe – comment on which occurred the most often or least often

12. Graphs for numerical data

13. Dotplot Used with numerical data (either discrete or continuous)
Made by putting dots (or X’s) on a number line
Can make comparative dotplots by using the same axis for multiple groups

14. Types (shapes) of Distributions

15. Symmetrical
refers to data in which both sides are (more or less) the same when the graph is folded vertically down the middle
bell-shaped is a special type
has a center mound with two sloping tails

16. Uniform
refers to data in which every class has equal or approximately equal frequency

17. Skewed (left or right)
refers to data in which one side (tail) is longer than the other side
the direction of skewness is on the side of the longer tail

18. Bimodal (multi-modal)
refers to data in which two (or more) classes have the largest frequency & are separated by at least one other class

19. How to describe a numerical, univariate graph
Do after Features of Distributions Activity

20. What strikes you as the most distinctive difference among the distributions of exam scores in classes A, B, & C ?

21. 1. Center discuss where the middle of the data falls
three types of central tendency
mean, median, & mode

22. What strikes you as the most distinctive difference among the distributions of scores in classes D, E, & F?
Class

23. 2. Spread discuss how spread out the data is
refers to the variability of the data
Range, standard deviation, IQR

24. What strikes you as the most distinctive difference among the distributions of exam scores in classes G, H, & I ?

25. 3. Shape refers to the overall shape of the distribution
symmetrical, uniform, skewed, or bimodal

26. What strikes you as the most distinctive difference among the distributions of exam scores in class K ? K

27. 4. Unusual occurrences
outliers - value that lies away from the rest of the data
gaps
clusters
anything else unusual

28. 5. In context
You must write your answer in reference to the specifics in the problem, using correct statistical vocabulary and using complete sentences!

29. More graphs for numerical data

30. Stemplots (stem & leaf plots)
Used with univariate, numerical data
Must have key so that we know how to read numbers
Can split stems when you have long list of leaves
Can have a comparative stemplot with two groups
Would a stemplot be a good graph for the number of pieces of gun chewed per day by AP Stat students? Why or why not?
Would a stemplot be a good graph for the number of pairs of shoes owned by AP Stat students? Why or why not?

31. Histograms Used with numerical data Bars touch on histograms Two types
Discrete
Bars are centered over discrete values
Continuous
Bars cover a class (interval) of values
For comparative histograms – use two separate graphs with the same scale on the horizontal axis
Would a histogram be a good graph for the fastest speed driven by AP Stat students? Why or why not?
Would a histogram be a good graph for the number of pieces of gum chewed per day by AP Stat students? Why or why not?

32. Cumulative Relative Frequency Plot (Ogive)
. . . is used to answer questions about percentiles.
Percentiles are the percent of individuals that are at or below a certain value.
Quartiles are located every 25% of the data. The first quartile (Q1) is the 25th percentile, while the third quartile (Q3) is the 75th percentile. What is the special name for Q2?
Interquartile Range (IQR) is the range of the middle half (50%) of the data.
IQR = Q3 – Q1