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 %

Explanation:

Step1: Count scores in 82 - 87

Scores: 83, 80, 83, 85, 83, 85, 87, 80. Wait, no, let's list all scores: 97, 69, 78, 80, 83, 73, 80, 68, 85, 69, 83, 77, 73, 89, 83, 74, 74, 85, 87, 97. Now filter 82 - 87: 83, 85, 83, 83, 85, 87. Wait, 80 is 80 (below 82), 89 is above 87. So 83 (3 times), 85 (2 times), 87 (1 time). Total: 3 + 2 + 1 = 6? Wait no, let's check each score:

80: 80 < 82? No, 80 is 80, 82 - 87: 82 ≤ x ≤ 87. So 83 (yes), 80 (no), 83 (yes), 85 (yes), 83 (yes), 85 (yes), 87 (yes). Wait, original scores: 80, 83, 80, 85, 83, 83, 85, 87. Wait, let's list all scores in 82 - 87:

83: appears 3 times (positions: 4, 10, 14), 85: 2 times (positions: 8, 17), 87: 1 time (position: 18). Also, check 80: 80 is 80, which is below 82? No, 80 is less than 82? 82 - 87: 82 to 87, so 82 ≤ score ≤ 87. So 80 is 80 (no), 83 is 83 (yes), 80 (no), 85 (yes), 83 (yes), 83 (yes), 85 (yes), 87 (yes). Wait, also, is there 82? No. So count: 83 (3), 85 (2), 87 (1). Total: 3 + 2 + 1 = 6? Wait, wait the scores: 80, 83, 80, 85, 83, 83, 85, 87. Wait, that's 8 scores? Wait no, original list has 20 scores? Wait no, the given scores: 97, 69, 78, 80, 83, 73, 80, 68, 85, 69, 83, 77, 73, 89, 83, 74, 74, 85, 87, 97. Let's count: 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. So 20 scores. Now, scores in 82 - 87:

83: positions 5, 11, 15 → 3 times.

85: positions 9, 18 → 2 times.

87: position 19 → 1 time.

80: positions 4, 7 → 80 < 82? 80 is 80, 82 - 87: 82 to 87, so 80 is below 82, so no. 89: position 14 → above 87, so no. So total in 82 - 87: 3 + 2 + 1 = 6? Wait, 3 + 2 + 1 = 6. Wait, but let's check again: 83 (3), 85 (2), 87 (1). 3 + 2 + 1 = 6. So frequency is 6.

Step2: Calculate relative frequency

Total scores: 20. Relative frequency = (frequency / 20) 100. So (6 / 20) 100 = 30%.

Step3: Calculate cumulative frequency

Previous cumulative frequency is 3 (from 88 - 93: cumulative 3). So 3 + 6 = 9.

Answer:

Frequency: 6, Relative Frequency: 30%, Cumulative Frequency: 9