1. Displaying Distributions with Graphs
Exploring Data
Displaying Distributions with Graphs

2. Vocab
Individuals- objects described by a set of data. Can be people, animals, or things
Variable- any characteristic of an individual. Can take different values for different individuals
Categorical Variable- places an individual into one of several groups or categories
Quantitative Variable- numerical values for which it makes sense to find an average

3. More Vocab
Distribution- of a variable tells us what values the variable takes and how often it takes these values
Inference- drawing conclusions that go beyond the data at hand

4. Data Analysis Graphical techniques (chapter 1.1)
Bar chart, pie chart, frequency table, stemplot, histogram, ogive, dotplot
Numerical techniques (chapter 1.2)
Mean, median, standard deviation, variance, IQR, range

5. Graphs for Categorical Data
Frequency Table- table that displays the count (frequency) of observations in each category or class
Relative Frequency Table- table that shows the percents (relative frequencies) of observations in each category or class
Pie Chart-displays all the categories that make up a whole, as a pie with slices that are sized by the counts or percents for the categories

6. Graphs for Categorical Data
Bar Graphs- the horizontal axis of a bar graph identifies the categories or quantities being compared. The graph is drawn with blank spaces between the bars to separate the items being compared
Two Way Table- table of counts that organizes data about two categorical variables

7. Two Way Table VOCAB Marginal Distribution Conditional Distribution
Distribution of values of that variable among all individuals described by the table
Conditional Distribution
The values of a variable among individuals who have a specific value of another variable
Association
between two variables is knowing the value of one variable to help predict the value of the other

8. Graphs for Quantitative Data
Stemplots- includes actual data values arranged in increasing order where the leaf is the last digit and the stem is the other portion of the number
Unreasonable with large data sets
Histogram- Bar graph for QUANTITATIVE DATA where bars all touch
Frequency/relative frequency
Frequency Table
Ogive- grouping observations into equal width classes; shows accumulating percent of observations as you move through the classes in increasing order
Dotplot- shows each data value as a dot above its location on a number line

9. Examining Distributions
Remember “SECS-C”
S = Shape
E = Extreme Values (Outliers)
C = Center
S = Spread
C = Context
Make meaningful descriptions and comparisons. Don’t just list numbers!
SECS-C is very important on free response!!!!!

10. Describing Shape
Symmetric- if the right and left sides of the graph are approximately mirror images of each other
Skewed- the tail on one end is much long than the other tail. The data values fall more on one side than the other.

11. Symmetric
On free response questions, never say the distribution is NORMAL! Always say approximately symmetric or mound shaped

12. Skewed to the Right
The right side of the graph is much longer than the left side
Most of the data values fall to the left side
The tail is to the right
The Mode is to the left, then comes the median, then the mean

13. Skewed to the Left
Left side of the graph is much longer than the right side
Most of the data falls to the right
The tail is to the left
The mean is to the left, then the median, then the mode

14. Summary

15. Other Shapes- Uniform

16. Other Shapes- Unimodal
One Mode

17. Other Shapes- Bimodal
2 modes

18. Using Histograms Wisely
Don’t confuse histograms with bar graphs. Histograms are for quantitative data that is grouped by classes and bar graphs are for categorical data
Use percents instead of actual frequencies when comparing 2 or more distributions
When creating a histogram on the ti-84, include labels and title when transferring on paper! (pg or Chapter 2 Lesson 2 Part 3 from Statistics R PowerPoints on my webpage)