6 lbs Assuming thataverage refers to the mean which of the f

6 lbs. Assuming thataverage 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 month at least one of their patients lost exactly

6 lbs.

Last month, the number of their clients who lost

6 lbs or less was equal to the number of their clients who lost 6 lbs or more.

Last month some of their patients lost less than 4 lbs.

This month some of their patients will lose at least 6 lbs.

None of the above statements is true.

Solution

The average loss of weight last month for the clinic\'s patients was 6 lbs. Since the average refers to the mean, the reference is to the simple average and not the weighted average. This means that the total weight loss last month of all the patients together, divided by 6 was 6lbs. Thus if 9 patients together lost 54 lbs, the average weight loss was 54/9 = 6lbs. Some patients could have lost more than 6 lbs and some patients could have lost less than 6 lbs. It is also possible that some patients lost exactly 6 lbs. However, none of the given statements is necessarily true:

1. Last month all of their patients lost at least 6 lbs. : If this were true, then the average weight loss would be more than 6lbs

2. Last month at least one of their patients lost exactly 6 lbs : This is possible but not necessarily true. Some patients could have lost more than 6 lbs and some patients could have lost less than 6 lbs.

3. Last month, the number of their clients who lost 6 lbs or less was equal to the number of their clients who lost 6 lbs or more: This statemene need not be true. In the example given above, if 9 patients together lost 54 lbs, then the average weight loss was 6lbs, but 9 cannot be divided into 2 equal whole numbers.

4. Last month some of their patients lost less than 4 lbs.: This is possible, but not necessarily true. If 2 patients lost 5 lbs each and 2 patients lost 7 lbs each, the average weight loss will be 6 lbs. We may observe that, here, no patient lost less than 4 lbs.

5.This month some of their patients will lose at least 6 lbs.: This statement is again not necessarily true. A weight loss of 6lbs per patient last month does not guarantee any weight loss this month.

Thus the only correct statement is that None of the above statements is true.