Question

analyzing student work
joseph completed the two - way table on the left about the social networking habits of his classmates as follows:
step 1: 85 - 30 = 5
step 2: 80 - 55 = 2
step 3: 140 - 80 =
step 4: 60 - 30 = 3
step 5: 25 + 30 = 5
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
(the two - way table has columns: site 2, no site 2, total; rows: site 1, no site 1, total. in site 1 row: site 2 is step 1, no site 2 is step 2, total is 80. in no site 1 row: site 2 is 30, no site 2 is step 4, total is step 3. in total row: site 2 is 85, no site 2 is step 5, total is 140.)

Explanation:

Step 1: Analyze Step 1

For the "Site 1" and "Site 2" cell (Step 1), total for Site 2 column is 85, and "No Site 1" & "Site 2" is 30. So \( 85 - 30 = 55 \), but Joseph got 5 (probably a typo, maybe 55). Wait, but let's check each step.

Step 2: Analyze Step 2

"Site 1" and "No Site 2" (Step 2): total for Site 1 row is 80, "Site 1" & "Site 2" (Step 1 should be 55? Wait, maybe original Step 1: 85 - 30 = 55 (correct formula, but Joseph wrote 5? Wait, the problem says Step 1: 85 - 30 = 5 (maybe 55, but typo). Then Step 2: 80 - 55 = 25 (if Step 1 was 55, then 80 - 55 = 25, but Joseph's Step 2: 80 - 55 = 2? No, maybe I misread. Wait, let's check Step 3: Total students is 140, Site 1 total is 80, so "No Site 1" total should be \( 140 - 80 = 60 \). So Step 3: 140 - 80 = 60 (correct formula, what did Joseph get? The problem says "Step 3: 140 - 80 = " (maybe he got wrong, but let's check Step 4: "No Site 1" & "No Site 2" (Step 4): "No Site 1" total is 60, "No Site 1" & "Site 2" is 30, so \( 60 - 30 = 30 \). Joseph's Step 4: 60 - 30 = 3 (wrong, should be 30). Wait, no, let's re-express the two - way table:

Columns: Site 2, No Site 2, Total

Rows: Site 1, No Site 1, Total

- Site 2 column total: 85 (Total row, Site 2)
- No Site 1 row, Site 2: 30 (No Site 1, Site 2)
- Site 1 row total: 80 (Site 1, Total)
- Total total: 140 (Total, Total)
- No Site 2 column total: Step 5 (Site 2 column total + No Site 2 column total = 140, so No Site 2 total = 140 - 85 = 55? Wait, no, rows: Site 1 total 80, No Site 1 total = 140 - 80 = 60 (Step 3: correct formula is 140 - 80 = 60. If Joseph did Step 3 as 140 - 80 = x, let's see Step 4: No Site 1 row, No Site 2: No Site 1 total (60) minus No Site 1, Site 2 (30) = 30. So Step 4: 60 - 30 = 30. If Joseph did 60 - 30 = 3, that's wrong. But let's check Step 5: No Site 2 column total: Site 1, No Site 2 (Step 2) + No Site 1, No Site 2 (Step 4) = Step 5. So Step 2 (Site 1, No Site 2) + Step 4 (No Site 1, No Site 2) = Step 5 (No Site 2 total). Site 1, No Site 2: Step 2, Site 1 total (80) - Site 1, Site 2 (Step 1) = 80 - Step 1. Step 1: Site 2 column total (85) - No Site 1, Site 2 (30) = 55. So Step 1 should be 55, Step 2: 80 - 55 = 25, Step 4: 60 - 30 = 30, Step 5: 25 + 30 = 55. Now check Joseph's steps:

- Step 1: 85 - 30 = 5 (wrong, should be 55)
- Step 2: 80 - 55 = 2 (wrong, should be 25)
- Step 3: 140 - 80 = (let's say he got 60, correct formula, but maybe he miscalculated? Wait, the problem's dropdown is about which step has error. Wait, let's check Step 4: 60 - 30 = 3 (wrong, should be 30). But maybe the key is Step 4: 60 - 30 = 30 is correct formula, but Joseph did 60 - 30 = 3 (error). Wait, no, let's re - evaluate:

Wait, the two - way table structure:

| | Site 2 | No Site 2 | Total |
|----------------|--------|-----------|-------|
| Site 1 | Step 1 | Step 2 | 80 |
| No Site 1 | 30 | Step 4 | Step 3|
| Total | 85 | Step 5 | 140 |

1. Step 1: Site 1 & Site 2 = Total Site 2 - No Site 1 & Site 2 = \( 85 - 30 = 55 \). If Joseph did 85 - 30 = 5 (error here? But maybe typo, 55).
2. Step 2: Site 1 & No Site 2 = Total Site 1 - Site 1 & Site 2 = \( 80 - 55 = 25 \). If Joseph did 80 - 55 = 2 (error).
3. Step 3: Total No Site 1 = Total - Total Site 1 = \( 140 - 80 = 60 \). Correct formula, if he calculated right, no error.
4. Step 4: No Site 1 & No Site 2 = Total No Site 1 - No Site 1 & Site 2 = \( 60 - 30 = 30 \). If Joseph did 60 - 30 = 3 (error).
5. Step 5: Total No Site 2 = Site 1 & No Site 2 + No Site 1 & No Site 2 = \( 25 + 30 = 55 \). If Joseph did 25 + 30 = 5 (error, but 25 + 30 = 55).

Wait, the problem's dropdown options: "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".

Let's check each step's formula and result:

- Step 1: Formula \( 85 - 30 \) is correct (to find Site 1 & Site 2). \( 85 - 30 = 55 \), if Joseph wrote 5 (maybe a typo, 55), but the step says "85 - 30 = 5" (so error here? But maybe I misread the step. Wait, the user's image shows Step 1: 85 - 30 = 5 (probably 55, but he got 5). So error in Step 1? No, wait Step 4: 60 - 30 = 3 (should be 30). Wait, let's recast:

Total No Site 1 (Step 3) = 140 - 80 = 60 (correct formula). Then Step 4: No Site 1 & No Site 2 = 60 - 30 = 30. If Joseph did 60 - 30 = 3, that's error in Step 4. But maybe the key is Step 4. Wait, no, let's check Step 5: 25 + 30 = 55, if Joseph did 25 + 30 = 5, error in Step 5. But the options are as given. Wait, maybe the correct error is in Step 4? Wait, no, let's do step by step:

1. Step 1: Calculate Site 1, Site 2. Total Site 2 is 85, No Site 1, Site 2 is 30. So \( 85 - 30 = 55 \). If Joseph's Step 1 is 85 - 30 = 5 (error, should be 55).
2. Step 2: Site 1, No Site 2 = Site 1 total (80) - Site 1, Site 2 (55) = \( 80 - 55 = 25 \). If Joseph's Step 2 is 80 - 55 = 2 (error, should be 25).
3. Step 3: No Site 1 total = Total (140) - Site 1 total (80) = \( 140 - 80 = 60 \). Correct formula, so if he calculated 60, no error.
4. Step 4: No Site 1, No Site 2 = No Site 1 total (60) - No Site 1, Site 2 (30) = \( 60 - 30 = 30 \). If Joseph's Step 4 is 60 - 30 = 3 (error, should be 30).
5. Step 5: No Site 2 total = Site 1, No Site 2 (25) + No Site 1, No Site 2 (30) = \( 25 + 30 = 55 \). If Joseph's Step 5 is 25 + 30 = 5 (error, should be 55).

But the problem's dropdown has "an error in Step 4" as an option? Wait, maybe the original problem's Step 4 is 60 - 30 = 3 (wrong, should be 30), so error in Step 4. But let's check the formula for each step:

- Step 1: Correct formula (85 - 30), result wrong (5 instead of 55) → error.
- Step 2: Correct formula (80 - 55), result wrong (2 instead of 25) → error.
- Step 3: Correct formula (140 - 80), result should be 60 → if he did that, no error.
- Step 4: Correct formula (60 - 30), result wrong (3 instead of 30) → error.
- Step 5: Correct formula (25 + 30), result wrong (5 instead of 55) → error.

But maybe the intended error is in Step 4? Wait, no, let's see the two - way table's No Site 2 column total: Site 2 total is 85, so No Site 2 total is 140 - 85 = 55. Step 5 is Site 1, No Site 2 (Step 2) + No Site 1, No Site 2 (Step 4) = 55. If Step 2 is 25 and Step 4 is 30, 25 + 30 = 55 (correct). But if Step 4 is 3, 25 + 3 = 28 ≠ 55. So Step 4 has error.

Wait, the user's problem: Joseph's steps:

Step 1: 85 - 30 = 5 (error, should be 55)

Step 2: 80 - 55 = 2 (error, should be 25)

Step 3: 140 - 80 = (let's say 60, correct)

Step 4: 60 - 30 = 3 (error, should be 30)

Step 5: 25 + 30 = 5 (error, should be 55)

But the dropdown options include "an error in Step 4". So the answer is an error in Step 4.

Answer:

an error in Step 4