Question

a chemical technician measured the temperatures (in °c) of 13 different solutions. the temperatures are shown below. complete the grouped relative frequency distribution for the data. (note that we are using a class width of 4.) write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage.
temperature (in °c)
102 109 104 103 101
95 108 99 94 97
93 100 102

temperature (in °c) | relative frequency
93 to 96 |
97 to 100 |
101 to 104 |
105 to 108 |
109 to 112 |

Explanation:

Step1: Count total data points

There are 13 data points (since 13 different solutions).

Step2: Count for each class

• 93 to 96: Temperatures are 93, 95, 94. So count = 3.
• 97 to 100: Temperatures are 97, 99, 100. So count = 3.
• 101 to 104: Temperatures are 101, 103, 104, 102, 102. Wait, wait, original data: 102, 109, 104, 103, 101, 95, 108, 99, 94, 97, 93, 100, 102. Wait, let's list all 13: 102, 109, 104, 103, 101, 95, 108, 99, 94, 97, 93, 100, 102. So:
• 93 - 96: 93, 95, 94 → 3
• 97 - 100: 97, 99, 100 → 3
• 101 - 104: 101, 103, 104, 102, 102 → 5 (Wait, 101,103,104,102,102: that's 5? Wait 102 appears twice, 101,103,104: total 5? Wait 101,103,104,102,102: 5 numbers.
• 105 - 108: 108 (wait, 108 is there, and any others? 105? No. So 108 is one? Wait original data: 108, 109? Wait no, 108 is in 105 - 108? Wait 105 to 108: temperatures between 105 (inclusive) and 108 (inclusive). So 108 is there, any others? 105? No. Wait 108 is one? Wait no, 108 is 108, so 105 - 108: 108. Wait no, 108 is 108, so 105 ≤ x ≤ 108. So 108 is in, any others? 105? No. Wait 108 is one? Wait original data: 108, 109, 104, 103, 101, 95, 108, 99, 94, 97, 93, 100, 102. Wait 108 is once? Wait no, wait the data: let's list all 13:

1. 102
2. 109
3. 104
4. 103
5. 101
6. 95
7. 108
8. 99
9. 94
10. 97
11. 93
12. 100
13. 102

So:

• 93 - 96: 93 (11), 95 (6), 94 (9) → 3 numbers (positions 11,6,9)
• 97 - 100: 97 (10), 99 (8), 100 (12) → 3 numbers (positions 10,8,12)
• 101 - 104: 101 (5), 103 (4), 104 (3), 102 (1), 102 (13) → 5 numbers (positions 5,4,3,1,13)
• 105 - 108: 108 (7) → 1 number (position 7)
• 109 - 112: 109 (2) → 1 number (position 2)

Wait, wait, 3 + 3 + 5 + 1 + 1 = 13? 3+3=6, 6+5=11, 11+1=12, 12+1=13. Yes. So:

• 93 - 96: 3
• 97 - 100: 3
• 101 - 104: 5
• 105 - 108: 1
• 109 - 112: 1

Step3: Calculate relative frequency (count / total)

• 93 to 96: 3 / 13 ≈ 0.23 (rounded to nearest hundredth)
• 97 to 100: 3 / 13 ≈ 0.23
• 101 to 104: 5 / 13 ≈ 0.38
• 105 to 108: 1 / 13 ≈ 0.08
• 109 to 112: 1 / 13 ≈ 0.08

Wait, but let's recheck the 101 - 104 class. The temperatures in 101 - 104 (inclusive) are 101, 103, 104, 102, 102. So 101 (101), 103 (103), 104 (104), 102 (102), 102 (102). So 5 values. Correct.

So:

• 93 to 96: 3/13 ≈ 0.23
• 97 to 100: 3/13 ≈ 0.23
• 101 to 104: 5/13 ≈ 0.38
• 105 to 108: 1/13 ≈ 0.08
• 109 to 112: 1/13 ≈ 0.08

Answer:

• 93 to 96: 0.23
• 97 to 100: 0.23
• 101 to 104: 0.38
• 105 to 108: 0.08
• 109 to 112: 0.08