Displaying Distributions with Graphs Exploring Data Displaying Distributions with Graphs

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

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

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

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

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

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

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

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!!!!!

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.

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

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

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

Summary

Other Shapes- Uniform

Other Shapes- Unimodal One Mode

Other Shapes- Bimodal 2 modes

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. 59-60 or Chapter 2 Lesson 2 Part 3 from Statistics R PowerPoints on my webpage)