Question

video lesson 5.3 example 2 - finding joint and marginal relative frequencies

1. use the debate competition information in extra example 1 to make a two - way table that shows the joint and marginal relative frequencies.

(there are two tables in the image, one with empty cells for junior, senior, total rows and qualified, did not qualify, total columns, and another with junior: qualified 7, did not qualify 9; senior: qualified 19, did not qualify 5)
integrated math 2a
credit 5
30

Explanation:

Step1: Find Total Number of Students

First, we find the total number of students by adding all the joint frequencies. The number of junior qualified is 7, junior did not qualify is 9, senior qualified is 19, and senior did not qualify is 5. So total number of students \( n = 7 + 9 + 19 + 5 = 40 \).

Step2: Calculate Joint Relative Frequencies

• Junior - Qualified: \( \frac{7}{40} = 0.175 \)
• Junior - Did Not Qualify: \( \frac{9}{40} = 0.225 \)
• Senior - Qualified: \( \frac{19}{40} = 0.475 \)
• Senior - Did Not Qualify: \( \frac{5}{40} = 0.125 \)

Step3: Calculate Marginal Relative Frequencies for Rows

• Junior Total: \( \frac{7 + 9}{40} = \frac{16}{40} = 0.4 \)
• Senior Total: \( \frac{19 + 5}{40} = \frac{24}{40} = 0.6 \)

Step4: Calculate Marginal Relative Frequencies for Columns

• Qualified Total: \( \frac{7 + 19}{40} = \frac{26}{40} = 0.65 \)
• Did Not Qualify Total: \( \frac{9 + 5}{40} = \frac{14}{40} = 0.35 \)

Step5: Calculate Grand Total

The grand total (total of all marginal row totals or marginal column totals) should be 1. \( 0.4 + 0.6 = 1 \) (or \( 0.65 + 0.35 = 1 \))

Now we fill the two - way table with these relative frequencies:

	Qualified	Did Not Qualify	Total
Senior	0.475	0.125	0.6
Total	0.65	0.35	1

Answer:

The two - way table with joint and marginal relative frequencies is as follows:

	Qualified	Did Not Qualify	Total
Senior	0.475	0.125	0.6
Total	0.65	0.35	1