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. last month more than half of their patients lost at least 6 lb. last month at least one of their patients lost exactly 6 lb. last month at least one of their patients lost at least 6 lb. two months ago some of their patients lost at least 6 lb. last month some of their patients lost more than 4 lb. none of the above statements are true.

Explanation:

Step1: Analyze the concept of mean

The mean is the sum of all values divided by the number of values. Just because the mean weight - loss is 6 lb doesn't mean more than half of patients lost at least 6 lb. For example, a few patients could have lost a large amount while many lost less.

Step2: Consider the case of exact value

The mean being 6 lb doesn't guarantee that at least one patient lost exactly 6 lb. The values could be distributed in a way that no value is exactly 6 lb.

Step3: Analyze the "at least one" case

If the mean is 6 lb, it is possible that all patients lost less than 6 lb, so we can't say at least one patient lost at least 6 lb.

Step4: Consider the time - two months ago

The information given is about last month, so we can't make any conclusion about two months ago.

Step5: Analyze the "more than 4 lb" case

Suppose all patients lost 4 lb or less. Then the mean weight - loss would be 4 lb or less. Since the mean is 6 lb, some patients must have lost more than 4 lb.

Answer:

Last month some of their patients lost more than 4 lb.