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ADAPTED FROM WALCH EDUCATION Using Two-Way Frequency Tables

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Previously, you learned that there are two equivalent expressions for the conditional probability of B given A: Conditional probability can be used to test for independence. Events A and B are independent events if or if Key Concepts 7.2.2: Using Two-Way Frequency Tables2

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For real-world data, modified tests for independence are sometimes used: Events A and B are independent if the occurrence of A has no significant effect on the probability of B; that is, Events A and B are independent if the occurrence of B has no significant effect on the probability of A; that is, Continued 7.2.2: Using Two-Way Frequency Tables3

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If A and B are two events from a sample space with P(A) 0, then the conditional probability of B given A in set notation is The conditional probability formula can be solved to obtain this formula for P(A and B): Concepts, continued 7.2.2: Using Two-Way Frequency Tables4

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A two-way frequency table is a frequency table that shows two categories of characteristics, one in rows and the other in columns. Each cell value is a frequency that shows how many times two different characteristics appear together. Two-Way Frequency Table 7.2.2: Using Two-Way Frequency Tables5

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Typical Setup of a Two-Way Frequency Table 7.2.2: Using Two-Way Frequency Tables6 Category 1 of characteristics Category 2 of characteristics Characteristic 1Characteristic 2 Characteristic 1ab Characteristic 2cd

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When probabilities and conditional probabilities are calculated, then totals of characteristics are needed. Note: 7.2.2: Using Two-Way Frequency Tables7 Category 1 of characteristics Category 2 of characteristicsTotal Characteristic 1Characteristic 2 Characteristic 1ab Characteristic 2cd Total

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The Student Council wants to host a school-wide activity. Council members survey 40 students, asking them to choose either a field trip, a dance, or a talent show. The table on the following slides shows the survey results, with the surveyed students numbered 140. Construct a two-way frequency table to summarize the data. Practice: 7.2.2: Using Two-Way Frequency Tables8

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Table of Survey Results 7.2.2: Using Two-Way Frequency Tables9 (continued) StudentGradeActivityStudentGradeActivity 110FT1112D 2 D 10TS 310TS1311TS 410FT1410FT 511D1511D 612D1610FT 710TS1712D 810FT1810FT 910FT1912D 1011TS2011TS Key: TS = Talent show, FT = Field trip, D = Dance

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Table of Survey Results, continued 7.2.2: Using Two-Way Frequency Tables10 StudentGradeActivityStudentGradeActivity 2110D3112FT 2210FT3210TS 2312D3312D 2411D3411D 2511TS3511FT 2612D3611FT 2712D3711TS 2810D3812TS 2911D3911FT 3011D4012TS Key: TS = Talent show, FT = Field trip, D = Dance

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Set up a table that shows Grade and Activity choice as categories, and all the different characteristics in each category. Step 1 7.2.2: Using Two-Way Frequency Tables11 Grade Activity choice Talent showField tripDance 10 11 12

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For each student, draw a tally mark that corresponds to that students grade and choice of activity in the appropriate cell of the data table. The complete tally table below shows the tally marks for all the students. Step 2 7.2.2: Using Two-Way Frequency Tables12 Grade Activity choice Talent showField tripDance 10 11 12

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Create a two-way frequency table to show your count results (These results are frequencies). Step 3 7.2.2: Using Two-Way Frequency Tables13 Grade Activity choice Talent showField tripDance 10482 11536 12219

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MS. DAMBREVILLE Thanks For Watching