Question

the frequency table represents the job status of a number of high school students.
job status

	looking for job	not looking for job	total
not currently employed	38	72	110
total	50	100	150

which shows the conditional relative frequency table by column?
job status

	looking for job	not looking for job	total
not

Explanation:

Step1: Recall Conditional Relative Frequency by Column

To find the conditional relative frequency by column, we divide each cell value by the total of its column. The column totals are: "Looking for Job" column total = 50, "Not Looking for Job" column total = 100, and "Total" column (though for conditional relative frequency by column, we focus on the first two columns for the job status rows).

Step2: Calculate for "Currently Employed" Row

- For "Looking for Job" column: $\frac{12}{50} = 0.24$
- For "Not Looking for Job" column: $\frac{28}{100} = 0.28$
- For "Total" column (of this row): $\frac{40}{150} \approx 0.27$ (but actually, for conditional relative frequency by column, the total of each column's conditional frequencies should be 1. Wait, maybe I misspoke. Wait, conditional relative frequency by column: each entry in a column is divided by the column's total. So for "Currently Employed" row:
- Looking for Job: $12\div50 = 0.24$
- Not Looking for Job: $28\div100 = 0.28$
- Total (of the row's conditional frequencies by column): $0.24 + 0.28 = 0.52$? Wait, no, maybe the "Total" row is different. Wait, let's do "Not Currently Employed" row:
- Looking for Job: $38\div50 = 0.76$
- Not Looking for Job: $72\div100 = 0.72$
- Then, for each column, the sum of the two rows (Currently Employed and Not Currently Employed) should be 1 (since $0.24 + 0.76 = 1$ for "Looking for Job" column, and $0.28 + 0.72 = 1$ for "Not Looking for Job" column). Then the "Total" row (the bottom row) would be the column totals divided by the grand total? Wait, no, the "Total" column in the original table is 150, but for conditional relative frequency by column, the "Total" row (the bottom row of the conditional table) would be the column totals (50, 100, 150) divided by the grand total (150)? Wait, no, maybe the correct approach is:

Wait, the problem is asking which table shows the conditional relative frequency by column. Let's check the given option's first cell: "Currently Employed" and "Looking for Job" is 0.3? Wait, no, our calculation was 0.24. Wait, maybe I made a mistake. Wait, no, the user's given option has "Currently Employed" and "Looking for Job" as 0.3? Wait, no, maybe the original table's "Looking for Job" total is 50? Wait, 12 + 38 = 50, correct. 28 + 72 = 100, correct. 40 + 110 = 150, correct.

Wait, maybe the option (the one with "Currently Employed" row: Looking for Job = 0.24, Not Looking for Job = 0.28, Total ≈ 0.27; "Not Currently Employed" row: Looking for Job = 0.76, Not Looking for Job = 0.72, Total ≈ 0.73). But the user's partial option shows "Currently Employed" with Looking for Job = 0.3 (which is wrong, should be 0.24) but maybe a typo? Wait, no, maybe I miscalculated. Wait, 12 divided by 50: 12/50 = 0.24, yes. 28/100 = 0.28. 38/50 = 0.76, 72/100 = 0.72. Then the "Total" column for each row: 40/150 ≈ 0.27, 110/150 ≈ 0.73. So the correct conditional relative frequency table by column would have:

| Job Status | Looking for Job | Not Looking for Job | Total |
|---------------------|-----------------|---------------------|-------|
| Currently Employed | 12/50 = 0.24 | 28/100 = 0.28 | 40/150 ≈ 0.27 |
| Not Currently Employed | 38/50 = 0.76 | 72/100 = 0.72 | 110/150 ≈ 0.73 |
| Total | 50/150 ≈ 0.33 | 100/150 ≈ 0.67 | 150/150 = 1 |

But wait, the "Total" row in the conditional table by column: each column's total (50, 100, 150) divided by the grand total (150). So "Looking for Job" column total: 50/150 ≈ 0.33, "Not Looking for Job" column total: 100/150 ≈ 0.67, and "Total" column total: 150/150 = 1.

But the given option in the problem has "Currently Employed" and "Looking for Job" as 0.3, which is incorrect. Wait, maybe the user's table was cut off. Assuming the correct table (even though the given option's first cell is wrong, but maybe a miscalculation on my part? Wait, no, 12 divided by 50 is 0.24, not 0.3. Wait, maybe the column total is 40? No, the column total for "Looking for Job" is 50 (12 + 38). Wait, maybe the problem's table has a typo, but assuming we proceed, the correct conditional relative frequency by column would be:

For "Currently Employed" row:
- Looking for Job: 12/50 = 0.24
- Not Looking for Job: 28/100 = 0.28
- Total: 40/150 ≈ 0.27

For "Not Currently Employed" row:
- Looking for Job: 38/50 = 0.76
- Not Looking for Job: 72/100 = 0.72
- Total: 110/150 ≈ 0.73

And the "Total" row (the bottom row) would be:
- Looking for Job: 50/150 ≈ 0.33
- Not Looking for Job: 100/150 ≈ 0.67
- Total: 150/150 = 1

But since the user's option shows "Currently Employed" with Looking for Job as 0.3 (which is wrong), but maybe the intended correct table is the one where each cell is divided by its column total. So the correct conditional relative frequency table by column would have:

| Job Status | Looking for Job | Not Looking for Job | Total |
|---------------------|-----------------|---------------------|-------------|
| Currently Employed | 12/50 = 0.24 | 28/100 = 0.28 | 40/150 ≈ 0.27 |
| Not Currently Employed | 38/50 = 0.76 | 72/100 = 0.72 | 110/150 ≈ 0.73 |
| Total | 50/150 ≈ 0.33 | 100/150 ≈ 0.67 | 150/150 = 1 |

So if the option (the one with "Currently Employed" row: Looking for Job = 0.24, Not Looking for Job = 0.28, Total ≈ 0.27; "Not Currently Employed" row: Looking for Job = 0.76, Not Looking for Job = 0.72, Total ≈ 0.73) is the correct one. But since the user's given option has "Currently Employed" and "Looking for Job" as 0.3 (which is incorrect), maybe there was a mistake. Wait, maybe I misread the original table. Wait, original table: "Looking for Job" column: 12 (Currently Employed), 38 (Not Currently Employed), total 50. Correct. "Not Looking for Job" column: 28 (Currently Employed), 72 (Not Currently Employed), total 100. Correct. So 12/50 = 0.24, 28/100 = 0.28, 38/50 = 0.76, 72/100 = 0.72. So the correct conditional relative frequency table by column would have these values.

Answer:

The correct conditional relative frequency table by column is:

Job Status	Looking for Job	Not Looking for Job	Total
Not Currently Employed	0.76	0.72	≈ 0.73
Total	1.00	1.00	1.00

(Note: The "Total" row for each column should sum to 1, so for "Looking for Job" column: 0.24 + 0.76 = 1, for "Not Looking for Job" column: 0.28 + 0.72 = 1, and the "Total" column (the bottom row) is the column totals divided by the grand total, but typically in conditional relative frequency tables by column, the "Total" row for the job status rows is the sum of the conditional frequencies for that row, but actually, the correct way is as calculated above.)

If we consider the given option's partial data, the correct table (even though the first cell in the option was wrong) should have "Currently Employed" and "Looking for Job" as 0.24, "Not Looking for Job" as 0.28, "Not Currently Employed" and "Looking for Job" as 0.76, "Not Looking for Job" as 0.72, and the totals as ≈0.27 and ≈0.73 for the job status rows, and 1 for the column totals.