Question

joseph completed the two - way table on the left about the social networking habits of his classmates as follows: step 1: 85 - 30 = 55 step 2: 80 - 55 = 25 step 3: 140 - 80 = 60 step 4: 60 - 30 = 30 step 5: 25 + 30 = 55 the student made an error in step 1 an error in step 2 an error in step 3 an error in step 4 an error in step 5 no error

Explanation:

Step1: Analyze Step 1

The total for "Site 2" is 85, and "No Site 1" and "Site 2" is 30. So "Site 1" and "Site 2" should be \(85 - 30 = 55\), which matches Step 1. So Step 1 is correct.

Step2: Analyze Step 2

"Site 1" total is 80, "Site 1" and "Site 2" is 55. So "Site 1" and "No Site 2" should be \(80 - 55 = 25\), which matches Step 2. So Step 2 is correct.

Step3: Analyze Step 3

Total students are 140, "Site 1" total is 80. So "No Site 1" total should be \(140 - 80 = 60\), which matches Step 3. So Step 3 is correct.

Step4: Analyze Step 4

"No Site 1" total is 60, "No Site 1" and "Site 2" is 30. So "No Site 1" and "No Site 2" should be \(60 - 30 = 30\), which matches Step 4. Wait, but let's check Step 5.

Step5: Analyze Step 5

"Site 1" and "No Site 2" is 25, "No Site 1" and "No Site 2" is 30. So "No Site 2" total should be \(25 + 30 = 55\), which matches Step 5. Wait, but the initial thought about Step 4 was wrong? Wait no, let's re - check the two - way table structure.

Wait, the "No Site 2" column total: "Site 1" and "No Site 2" is 25, "No Site 1" and "No Site 2" is 30. So total "No Site 2" is \(25 + 30 = 55\). And the "Total" row: "Site 2" is 85, "No Site 2" is 55, so total is \(85 + 55 = 140\), which matches. But wait, the error is in Step 4? No, wait, let's re - examine the "No Site 1" row. "No Site 1" and "Site 2" is 30, "No Site 1" and "No Site 2" is 30, so "No Site 1" total is \(30+30 = 60\), which matches Step 3. But wait, the "Site 2" column: "Site 1" and "Site 2" is 55, "No Site 1" and "Site 2" is 30, so "Site 2" total is \(55 + 30 = 85\), which matches.

Wait, maybe I made a mistake. Wait, let's start over.

Two - way table structure:

Rows: Site 1, No Site 1, Total

Columns: Site 2, No Site 2, Total

We know:

- Site 1 row, Total column: 80

- No Site 1 row, Site 2 column: 30

- Total row, Site 2 column: 85

- Total row, Total column: 140

Step 1: Site 1, Site 2 = Total (Site 2) - No Site 1, Site 2 = \(85 - 30 = 55\) (correct)

Step 2: Site 1, No Site 2 = Site 1 (Total) - Site 1, Site 2 = \(80 - 55 = 25\) (correct)

Step 3: No Site 1 (Total) = Total (Total) - Site 1 (Total) = \(140 - 80 = 60\) (correct)

Step 4: No Site 1, No Site 2 = No Site 1 (Total) - No Site 1, Site 2 = \(60 - 30 = 30\) (correct)

Step 5: No Site 2 (Total) = Site 1, No Site 2 + No Site 1, No Site 2 = \(25+30 = 55\) (correct)

Wait, but the option marked is "an error in Step 4", but according to our analysis, all steps are correct? No, wait, maybe the table structure is different. Wait, maybe the "Total" row for "Site 2" is 85, "No Site 2" is Step 5, and total is 140. So "No Site 2" should be \(140 - 85 = 55\), which is what Step 5 gives. And "Site 1, No Site 2" is 25, "No Site 1, No Site 2" is 30, \(25 + 30 = 55\), correct. "No Site 1" total is 60, "No Site 1, Site 2" is 30, so "No Site 1, No Site 2" is \(60 - 30 = 30\), correct. "Site 1" total is 80, "Site 1, Site 2" is 55, so "Site 1, No Site 2" is \(80 - 55 = 25\), correct. "Site 2" total is 85, "No Site 1, Site 2" is 30, so "Site 1, Site 2" is \(85 - 30 = 55\), correct. "Total" is 140, "Site 1" is 80, so "No Site 1" is \(140 - 80 = 60\), correct. So there is no error? But the option "no error" is there. Wait, maybe the initial marking of "an error in Step 4" was wrong. Wait, let's check again.

Wait, the problem says "The student made..." and the options include "no error". Let's re - check each step:

Step 1: \(85 - 30 = 55\) (correct, as Site 2 total is 85, No Site 1 and Site 2 is 30, so Site 1 and Site 2 is 85 - 30)

Step 2: \(80 - 55 = 25\) (correct, Site 1 total is 80, Site 1 and Site 2 is 55, so Site 1 and No Site 2 is 80 - 55)

Step 3: \(140 - 80 = 60\) (correct, total is 140, Site 1 total is 80, so No Site 1 total is 140 - 80)

Step 4: \(60 - 30 = 30\) (correct, No Site 1 total is 60, No Site 1 and Site 2 is 30, so No Site 1 and No Site 2 is 60 - 30)

Step 5: \(25 + 30 = 55\) (correct, Site 1 and No Site 2 is 25, No Site 1 and No Site 2 is 30, so No Site 2 total is 25 + 30)

So all steps are correct, so the student made no error.

Answer:

no error