6 lbs . Assuming that average refers to the mean, which of the following claims

Question

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.

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

Last month some of their patients lost exactly 6 lbs.

Last month at least one of their patients lost less than 8 lbs.

Two months ago at least one of their patients lost at least 6 lbs.

Last month all of their patients lost 6 lbs or more.

None of the above statements is true.

A weight-loss clinic advertised that last month its patients, on average, lost

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.

Explanation / Answer

As per the advertisement made by the weight loss clinic, its patients, on an average, lost 6 lbs last month. This means that some of their patients lost more than 6 lbs, some lost less than 6 lbs, possibly ( this may or may not be true) some lost exactly 6 lbs and that the mean of the data of weight loss was 6 lbs. Thus, the following statementsare true:

A. Last month at least one of their patients lost less than 8 lbs ( for otherwise, the mean would not be 6 lbs)

The following statements are apparently untrue:

B 6 lbs was equal to the number of their clients who lost more than 6 lbs.( This is meaningless)

C Two months ago at least one of their patients lost at least 6 lbs. ( this is irrelevant as the question is about weight loss in the last month)

D Last month all of their patients lost 6 lbs or more. ( this is apparently untrue as otherwise, the mean of the data would also be more than 6 lbs)

The statement " Last month some of their patients lost exactly 6 lbs" may or may not be true. If the weihted average of patients losing more than 6lbs equals the weighted average of patients losing less than 6 lbs, then the mean of the data is 6 lbs without any patient losing exactly 6 lbs.

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