Lesson 2 9/4/12

Do Now: Represent this data graphically 9/4/12 Lesson 2 Do Now: Represent this data graphically Siblings Erika 1 Samuel 2 Ryan Nicky Tia Pop. Home Town Erika 1,200,000 Samuel 5,000 Ryan Nicky 20,000,000 Tia 8,000

Homework: Read chapters 2 and 3 Answer CIRCLED questions on hand-out: They are on pg.38-40 of book, #6,8,13,18,22,24

Frequency Table Name Pairs of Shoes Sam 4 Erika 16 Tia 12 Ryan 6 Nicky 21 A Frequency Table organizes counts (data) by providing totals and category names. A bar chart displays the distribution of a categorical variable, showing the counts for each category next to each other for easy comparison

Relative Frequency Table Name Pairs of Shoes % Total Shoes Sam 4 6.78% Erika 16 27.12% Tia 12 20.34% Ryan 6 10.17% Nicky 21 35.59% Name Pairs of Shoes Sam 4 Erika 16 Tia 12 Ryan 6 Nicky 21 A relative frequency table displays the percentages, rather than the counts, of the values in each category.

Pie Charts Titanic Passengers Pie charts show the whole group of cases as a circle How easy is it to tell there are almost twice as many third-class passengers as first class passengers?

Comparing Displays Titanic Passengers

Categorical Data Condition Data must be counts or percentages of individual categories No Overlap!

Area Principle The area occupied by a part of the graph should correspond to the magnitude of the value it represents

Contingency Table   Right Handed Left Handed Totals Males 43 9 52 Females 44 4 48 87 13 100 In order to look at two categorical variables together we often arrange counts in a two-way table. The margins of a contingency table hold the frequency distributions for the data, for each variable this is called the marginal distribution   Right Handed Left Handed Totals Males 43% 9% 52% Females 44% 4% 48% 87% 13% 100%

Conditional Distributions If we look at each row separately we can see the distribution of left/right handedness under the condition of gender These percentages are called Conditional Distributions Why?   Right Handed Left Handed Totals Males 43 9 52 82.69% 17.31% 100% Females 44 4 48 91.67% 8.33%

Conditional Distributions (Cont.) We can turn our conditional distribution around and look at gender for each type of handedness. What is the new “Who”?   Right Handed Left Handed Totals Males 43 9 52 49.43% 69.23% 52% Females 44 4 48 50.57% 30.77% 48% 87 13 100 100%

Conditional Distributions Is your handedness dependent on your gender? Probably not. These two variables appear to be independent.

Segmented Bar Chart

Fin HW: Handout