Question

use 6-point bins (94 to 99, 88 to 93, etc.) to make a frequency table for the set of exam scores shown below. include columns for relative frequency and cumulative frequency. 97 69 78 80 83 73 80 68 85 69 83 77 73 89 83 74 74 85 87 97 complete the frequency table below. scores frequency relative frequency cumulative frequency 94 to 99 2 10 % 2 88 to 93 1 5 % 3 82 to 87 6 30 % 9 76 to 81 %

Explanation:

Step1: Count total number of scores

First, we count the total number of exam scores. Let's list them: 97, 69, 78, 80, 83, 73, 80, 68, 85, 69, 83, 77, 73, 89, 83, 74, 74, 85, 87, 97. So there are 20 scores.

Step2: Determine frequency for 76 to 81

Now, we identify the scores in the range 76 to 81. The scores are 78, 80, 80, 77. Wait, wait, let's check again. Wait, 76 to 81: let's list each score and see:

97 (94-99), 69 (below 76), 78 (76-81), 80 (76-81), 83 (82-87), 73 (below 76), 80 (76-81), 68 (below 76), 85 (82-87), 69 (below 76), 83 (82-87), 77 (76-81), 73 (below 76), 89 (88-93), 83 (82-87), 74 (below 76), 74 (below 76), 85 (82-87), 87 (82-87), 97 (94-99). Wait, no, wait the bins are 6-point: 94-99, 88-93, 82-87, 76-81, 70-75, 64-69? Wait, but the given bins are 94-99, 88-93, 82-87, 76-81. Wait, maybe I missed the lower bins, but the problem says "use 6-point bins (94 to 99, 88 to 93, etc.)", so the next bin after 82-87 is 76-81, then 70-75, 64-69, etc. But in the given table, the bins are 94-99, 88-93, 82-87, 76-81. So let's count the scores in 76-81: 78, 80, 80, 77. Wait, 78, 80, 80, 77: that's 4? Wait no, let's list all scores:

1. 97
2. 69
3. 78
4. 80
5. 83
6. 73
7. 80
8. 68
9. 85
10. 69
11. 83
12. 77
13. 73
14. 89
15. 83
16. 74
17. 74
18. 85
19. 87
20. 97

Now, scores in 76-81: 78 (3), 80 (4), 80 (5), 77 (12). Wait, 78, 80, 80, 77: that's 4 scores? Wait 78, 80, 80, 77: yes, 4. Wait but let's check the total frequency so far: 94-99: 2, 88-93:1, 82-87: let's count 83 (5), 85 (9), 83 (11), 83 (15), 85 (18), 87 (19): that's 6, which matches the table. Then 76-81: let's see, 78 (3), 80 (4), 80 (7), 77 (12): so 78, 80, 80, 77: that's 4. Wait, but total frequency should be 20. Let's check: 94-99:2, 88-93:1, 82-87:6, so 2+1+6=9. Then 76-81: let's see, the remaining scores: total 20, so 20 - (2+1+6) = 11? Wait no, that can't be. Wait I must have made a mistake. Wait let's list all scores and assign to bins:

Bin 94-99: 97, 97 → 2 (correct)
Bin 88-93: 89 → 1 (correct)
Bin 82-87: 83, 85, 83, 83, 85, 87 → let's count: 83 (5), 85 (9), 83 (11), 83 (15), 85 (18), 87 (19): that's 6 (correct)
Now, remaining scores: 69, 78, 80, 73, 80, 68, 69, 77, 73, 74, 74. Wait, that's 11 scores? Wait no, total is 20. 2 (94-99) +1 (88-93)+6 (82-87) =9. So 20-9=11. But the bin 76-81: let's see which of these remaining are in 76-81: 78, 80, 80, 77. The rest are below 76: 69,73,68,69,73,74,74. Wait, 78,80,80,77: that's 4. Then the next bin (70-75) would be 73,73,74,74: 4. Then 64-69: 69,68,69:3. Wait but the given table only has up to 76-81. Wait maybe the problem's table is missing lower bins, but we need to find frequency for 76-81. Wait let's re-express:

Wait the scores in 76-81: 78, 80, 80, 77. Wait, 78 is 78, 80 is 80, 80 is 80, 77 is 77. So that's 4 scores? Wait no, wait 76 to 81: inclusive? So 76 ≤ score ≤81. So 78,80,80,77: yes, 4. Wait but let's check the total frequency. Wait 2 (94-99) +1 (88-93)+6 (82-87)+4 (76-81) =13. Then the remaining scores: 69,73,68,69,73,74,74: 7 scores? Wait no, 20-13=7. But maybe I made a mistake in the bin ranges. Wait the bin 76-81: 76 to 81, so 76,77,78,79,80,81. So scores: 77,78,80,80. That's 4. So frequency is 4.

Step3: Calculate relative frequency

Relative frequency is frequency divided by total (20). So 4/20 = 0.2, which is 20%.

Step4: Calculate cumulative frequency

Cumulative frequency is the sum of frequencies up to that bin. So previous cumulative frequency is 9 (from 94-99:2, 88-93:1, 82-87:6; 2+1+6=9). Then add the frequency of 76-81 (4): 9+4=13.

Wait, but let's verify again. Wait the total number of scores: let's count again. The list:

1. 97
2. 69
3. 78
4. 80
5. 83
6. 73
7. 80
8. 68
9. 85
10. 69
11. 83
12. 77
13. 73
14. 89
15. 83
16. 74
17. 74
18. 85
19. 87
20. 97

Yes, 20 scores. Now, bin 94-99: 97,97 → 2 (cumulative 2)
Bin 88-93: 89 →1 (cumulative 2+1=3)
Bin 82-87: 83,85,83,83,85,87 →6 (cumulative 3+6=9)
Bin 76-81: 78,80,80,77 →4 (cumulative 9+4=13)
Then the remaining scores: 69,73,68,69,73,74,74 →7, which would be in 70-75 (73,73,74,74) and 64-69 (69,68,69), but the table only goes up to 76-81. So the frequency for 76-81 is 4, relative frequency is 4/20=20%, cumulative frequency is 9+4=13.

Wait, but the initial table had 94-99:2, 88-93:1, 82-87:6, so cumulative 9. Then 76-81: frequency 4, relative frequency 4/20=20%, cumulative 9+4=13.

Answer:

For the "76 to 81" bin:

• Frequency: 4
• Relative Frequency: 20%
• Cumulative Frequency: 13

So filling in the table:
Scores | Frequency | Relative Frequency | Cumulative Frequency
--- | --- | --- | ---
94 to 99 | 2 | 10% | 2
88 to 93 | 1 | 5% | 3
82 to 87 | 6 | 30% | 9
76 to 81 | 4 | 20% | 13

(Note: The question was about filling the blanks for 76 to 81, so the frequency is 4, relative frequency 20%, cumulative frequency 13.)