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14 Mar 2025, 20:40
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The mean Chance of Rain equals the mode of the set of Chance of Rain values.: Yes
If the high temperature is less than 80°F, then the low temperature is greater than 60°F.: No
The median high temperature is 11° higher than the highest low temperature.: No
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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35%
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The table shows a city’s 10-day weather forecast.
For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table. Otherwise, select No.
Temperature (degrees Fahrenheit) | ||||
| Day | High | Low | Chance of Rain | Wind Speed (mph) |
|---|---|---|---|---|
| 31-May | 80° | 59° | 10% | 9 |
| 1-Jun | 79° | 66° | 30% | 17 |
| 2-Jun | 77° | 63° | 20% | 13 |
| 3-Jun | 75° | 62° | 10% | 11 |
| 4-Jun | 71° | 60° | 10% | 10 |
| 5-Jun | 73° | 61° | 30% | 8 |
| 6-Jun | 74° | 60° | 30% | 6 |
| 7-Jun | 76° | 62° | 20% | 6 |
| 8-Jun | 82° | 64° | 20% | 7 |
| 9-Jun | 81° | 62° | 20% | 6 |
For each of the following statements, select Yes if the statement can be shown to be true based on the information in the table. Otherwise, select No.
| Yes | No | |
| The mean Chance of Rain equals the mode of the set of Chance of Rain values. | ||
| If the high temperature is less than 80°F, then the low temperature is greater than 60°F. | ||
| The median high temperature is 11° higher than the highest low temperature. |
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Official Answer
The mean Chance of Rain equals the mode of the set of Chance of Rain values.: Yes
If the high temperature is less than 80°F, then the low temperature is greater than 60°F.: No
The median high temperature is 11° higher than the highest low temperature.: No
poojaarora1818
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Updated on: 17 Mar 2025, 14:45
Originally posted by poojaarora1818 on 14 Mar 2025, 21:02.
Last edited by poojaarora1818 on 17 Mar 2025, 14:45, edited 2 times in total.
Last edited by poojaarora1818 on 17 Mar 2025, 14:45, edited 2 times in total.
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Solution:
1. The mean Chance of Rain equals the mode of the set of Chance of Rain values. Yes
Mean = \(\frac{10+30+20+10+10+30+30+20+20+20}{10}\) = 20
Mode = 20
2. If the high temperature is less than 80°F, then the low temperature is greater than 60°F. No
We can see that when the high temperatures on the 6th of June and 4th of June are 74 degrees and 71 degrees, then the low temperatures are 60 degrees on both days.
3. The median high temperature is 11° higher than the highest low temperature. No
Median = \(\frac{76 + 77}{2}\) = 76.5
The difference between the median of 76.5 and the higher low temperature which is 66 is 10.5.
1. The mean Chance of Rain equals the mode of the set of Chance of Rain values. Yes
Mean = \(\frac{10+30+20+10+10+30+30+20+20+20}{10}\) = 20
Mode = 20
2. If the high temperature is less than 80°F, then the low temperature is greater than 60°F. No
We can see that when the high temperatures on the 6th of June and 4th of June are 74 degrees and 71 degrees, then the low temperatures are 60 degrees on both days.
3. The median high temperature is 11° higher than the highest low temperature. No
Median = \(\frac{76 + 77}{2}\) = 76.5
The difference between the median of 76.5 and the higher low temperature which is 66 is 10.5.
Bismuth83
14 Mar 2025, 21:42
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Step 1. The mean Chance of Rain equals the mode of the Chance of Rain values set.
The Chance of Rain percentages are: 10%, 30%, 20%, 10%, 10%, 30%, 30%, 20%, 20%, 20%.
Mode: The most frequently occurring value is 20%, which appears 4 times.
Mean: Sum of all values divided by the total number of values:
\( \text{Mean} = \frac{10 + 30 + 20 + 10 + 10 + 30 + 30 + 20 + 20 + 20}{10} = \frac{200}{10} = 20\%\)
Conclusion: Yes, the mean equals the mode.
Step 2. If the high temperature is less than 80°F, then the low temperature is greater than 60°F.
High temperatures less than 80°F: 79°, 77°, 75°, 71°, 73°, 74°, 76°.
Corresponding low temperatures: 66°, 63°, 62°, 60°, 61°, 60°, 62°.
Observation: On 4-Jun and 6-Jun, the low temperature is exactly 60°F, which is not greater than 60°F.
Conclusion: No, the statement is not true.
Step 3. The median high temperature is 11° higher than the highest low temperature.
High temperatures: 80°, 79°, 77°, 75°, 71°, 73°, 74°, 76°, 82°, 81° (sorted: 71°, 73°, 74°, 75°, 76°, 77°, 79°, 80°, 81°, 82°).
Median high temperature: Average of the two middle values (76° and 77°):
\( \text{Median} = \frac{76 + 77}{2} = 76.5°\)
Highest low temperature: 66°.
Difference: 76.5 - 66 = 10.5°, not 11°.
Conclusion: No, the statement is not true.
Final Answers:
1. Yes
2. No
3. No
The Chance of Rain percentages are: 10%, 30%, 20%, 10%, 10%, 30%, 30%, 20%, 20%, 20%.
Mode: The most frequently occurring value is 20%, which appears 4 times.
Mean: Sum of all values divided by the total number of values:
\( \text{Mean} = \frac{10 + 30 + 20 + 10 + 10 + 30 + 30 + 20 + 20 + 20}{10} = \frac{200}{10} = 20\%\)
Conclusion: Yes, the mean equals the mode.
Step 2. If the high temperature is less than 80°F, then the low temperature is greater than 60°F.
High temperatures less than 80°F: 79°, 77°, 75°, 71°, 73°, 74°, 76°.
Corresponding low temperatures: 66°, 63°, 62°, 60°, 61°, 60°, 62°.
Observation: On 4-Jun and 6-Jun, the low temperature is exactly 60°F, which is not greater than 60°F.
Conclusion: No, the statement is not true.
Step 3. The median high temperature is 11° higher than the highest low temperature.
High temperatures: 80°, 79°, 77°, 75°, 71°, 73°, 74°, 76°, 82°, 81° (sorted: 71°, 73°, 74°, 75°, 76°, 77°, 79°, 80°, 81°, 82°).
Median high temperature: Average of the two middle values (76° and 77°):
\( \text{Median} = \frac{76 + 77}{2} = 76.5°\)
Highest low temperature: 66°.
Difference: 76.5 - 66 = 10.5°, not 11°.
Conclusion: No, the statement is not true.
Final Answers:
1. Yes
2. No
3. No
