An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements is true, mark the appropriate box. Last year fewer than half of their dlients made a profit of 10% or less. Two years ago some of their dients made a profit of at least 10%. Last year at least one of their dlients made a profit of 10% or more. Last year at least one of their dlients made a profit of exactly 10%. O Last year all of their clients made a profit of more than 5%. O None of the above statements are true.

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**Question Analysis Example for Educational Website**

**Scenario:**
An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that "average" refers to the mean, consider which of the following claims must be true based on this information.

**Note:** More than one statement could be true. If none of the statements is true, mark the appropriate box.

**Statements to Evaluate:**

1. Last year fewer than half of their clients made a profit of 10% or less.

2. Two years ago some of their clients made a profit of at least 10%.

3. Last year at least one of their clients made a profit of 10% or more.

4. Last year at least one of their clients made a profit of exactly 10%.

5. Last year all of their clients made a profit of more than 5%.

6. None of the above statements are true.

To analyze the validity of each statement based on the information provided:

1. **Last year fewer than half of their clients made a profit of 10% or less.**
   - This statement is checking whether the average necessarily indicates the distribution of profits among the clients.
   
2. **Two years ago some of their clients made a profit of at least 10%.**
   - This statement refers to a period that's not covered by the average mentioned and will need additional context from other data sources to validate.

3. **Last year at least one of their clients made a profit of 10% or more.**
   - To have an average of 10%, it is implied that there would be various profit levels among clients, implying that some clients must have made around or above 10%.

4. **Last year at least one of their clients made a profit of exactly 10%.**
   - This statement implies that there is a specific data point exactly at 10%, which is not a necessity for calculating a mean of 10%.

5. **Last year all of their clients made a profit of more than 5%.**
   - For an average (mean) to be 10%, it doesn't necessarily follow that all values must be substantially higher than a lower limit (such as 5%).

6. **None of the above statements are true.**
   - This option should be considered if it's determined that none of the other statements hold given the mean profit data presented.

**Diagram/Graphs Clarification:**

- There are no
Transcribed Image Text:**Question Analysis Example for Educational Website** **Scenario:** An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that "average" refers to the mean, consider which of the following claims must be true based on this information. **Note:** More than one statement could be true. If none of the statements is true, mark the appropriate box. **Statements to Evaluate:** 1. Last year fewer than half of their clients made a profit of 10% or less. 2. Two years ago some of their clients made a profit of at least 10%. 3. Last year at least one of their clients made a profit of 10% or more. 4. Last year at least one of their clients made a profit of exactly 10%. 5. Last year all of their clients made a profit of more than 5%. 6. None of the above statements are true. To analyze the validity of each statement based on the information provided: 1. **Last year fewer than half of their clients made a profit of 10% or less.** - This statement is checking whether the average necessarily indicates the distribution of profits among the clients. 2. **Two years ago some of their clients made a profit of at least 10%.** - This statement refers to a period that's not covered by the average mentioned and will need additional context from other data sources to validate. 3. **Last year at least one of their clients made a profit of 10% or more.** - To have an average of 10%, it is implied that there would be various profit levels among clients, implying that some clients must have made around or above 10%. 4. **Last year at least one of their clients made a profit of exactly 10%.** - This statement implies that there is a specific data point exactly at 10%, which is not a necessity for calculating a mean of 10%. 5. **Last year all of their clients made a profit of more than 5%.** - For an average (mean) to be 10%, it doesn't necessarily follow that all values must be substantially higher than a lower limit (such as 5%). 6. **None of the above statements are true.** - This option should be considered if it's determined that none of the other statements hold given the mean profit data presented. **Diagram/Graphs Clarification:** - There are no
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Follow-up Question
A weight-loss clinic advertised that last month its patients, on average, lost 6 lb. Assuming that average refers to the mean, which of the following claims must
be true based on this information?
Note: More than one statement could be true. If none of the statements are true, mark the appropriate box.
This month at least one of their patients will lose at least
6 lb.
Last month all of their patients lost more than 3 lb.
Last month some of their patients lost exactly 6 lb.
Last month fewer than half of their patients lost 6 lb or
less.
Last month at least one of their patients lost at least 6 lb.
None of the above statements are true.
X
Ś
Transcribed Image Text:A weight-loss clinic advertised that last month its patients, on average, lost 6 lb. Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements are true, mark the appropriate box. This month at least one of their patients will lose at least 6 lb. Last month all of their patients lost more than 3 lb. Last month some of their patients lost exactly 6 lb. Last month fewer than half of their patients lost 6 lb or less. Last month at least one of their patients lost at least 6 lb. None of the above statements are true. X Ś
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