Analyzing Goldfish Categorization and Distribution Data

1

1. On the paper plates or paper towels separate the goldfish by color 1. Yellow 2. Orange 3. Red and 4. Green 2. After every Goldfish is separated by color, then divide each color into two groups Goldfish with a face and Goldfish without a face 3. There will be a total of eight individual groups. 1. Yellow with a face 2. Yellow without a face 3. Orange with a face 4. Orange without a face 5. Red with a face 7. Green with a face 8. Green without a face 6. Red without a face 4. Count the number of Goldfish in each category. 2

Enter your totals into your two-way table. Answers will not be identical. Goldfish Goldfish With a Face With a Face Without Without a face a face Total Total Yellow Yellow 17 17 17 17 Orange Orange 6 6 6 6 Red Red 8 8 9 9 Green Green 9 9 9 9 Total Total 3

Total the number of Goldfish for each color by adding the rows. Total the number of Goldfish for face / no face by adding the columns. Again your individual answers will vary. Goldfish Goldfish With a Face With a Face Without Without a face a face Total Total Yellow Yellow 17 17 17 17 34 34 Orange Orange 6 6 6 6 12 12 Red Red 8 8 9 9 17 17 Green Green 9 9 9 9 18 18 Total Total 40 40 41 41 81 81 4

Marginal distribution of one of the categorical variables in a two-way table is the distribution of values of that variable among all individuals described by the table To find marginal distribution of a two way table divide each total in each cell by the total for the table and then multiple by 100. 5

Divide each total in each cell by the total for the table Multiple by 100. Goldfish Goldfish With a Face With a Face Without Without a face a face Total Total 17 / 81 =.2098 0.2098 100 = 20.98% Yellow Yellow 20.98% 41.96% 41.96% Orange Orange 7.41% 7.41% 14.82% 14.82% Red Red 9.88% 11.11% 20.99% 20.99% Green Green 11.11% 11.11% 22.22% 22.22% 40 / 81 49.38% 40 / 81 49.38% 41 / 81 50.61% 41 / 81 50.61% 81 / 81 100% Total Total 6

A conditional distribution of a variable is the distribution of values of that variable among only individuals who have a given value of the other variable. For example, if you pick a Goldfish with a face, what is the chance it is Yellow, or Orange, or Red, or Green? To find this divide each cell in the With Face row by the With Face Total and multiply by 100 7

Calculate the conditional distribution of Goldfish with a face. To find this divide each cell in the With Face column by the With Face Total and multiply by 100 Goldfish Goldfish With a Face With a Face Without Without a face a face Total Total Yellow Yellow 17 / 40 = 42.5% 17 / 40 = 42.5% Orange Orange 6 / 40 = 15% 6 / 40 = 15% Red Red 8 / 40 = 20% 8 / 40 = 20% Green Green 9 / 40 = 22.5% 9 / 40 = 22.5% Total Total 40 / 40 = 100% 40 / 40 = 100% 8

2 9

2 10

Insurance companies use information like the data from Activity Sheet 2 to find who is a higher risk when providing insurance. With auto insurance the more likely someone is to have an accident the higher risk that person is. Risk is the chance of loss or harm. If people are more likely to incur loss or harm, insurance companies are more likely to have to pay claims on those people. 11

A premium costs of a potential loss to a third party. premium is the fee paid now to transfer the A deductible person must pay per loss before the insurance company will pay a claim How are premiums and deductibles correlated to risk for insurance companies? Premiums and deductibles are based on the level of risk a policyholder is judged to be. The higher the risk, the higher premiums and deductibles will be. deductible is a fixed amount an insured 12

Driving Record Commute Type of Car Age Credit Score Marital Status Gender Grades 13