A weight-loss clinic advertised that last month its patients, on average, lost 7

Question

A weight-loss clinic advertised that last month its patients, on average, lost 7 lbs. 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 month at least one of their patients lost 7 lbs or more. This month at least one of their patients will lose at least 7 Ibs Last month, the number of their clients who lost more than 7 lbs was equal to the number of their clients who lost less than 7 Ibs Last month all of their patients lost less than 11 lbs Last month some of their patients lost exactly 7 bs None of the above statements is true

Explanation / Answer

a) This statement is true. For the average to be 7, either : 1) everyone gets a score of 7 or 2) if someone gets less than 7, someone has to get more than a 7. This statement corresponds to both scenarios where atleast one person either got an exact 7 or lesser than that.

b) This need not be true. Although it is highly possible, but there's no relation that we know that exists between last month and this month. This month's data can be totally different from last month.

c) This need not be true. For example, we can have 5 patients : 5, 6, 7, 7, 10. Here 2 clients lost less than 7 and 1 client loss more than 7.

d) This need not be true. For example, we can have 5 patients : 4, 5, 7, 7, 12. Here the mean is still 7 and a patient lost more than 11 lbs.

e) This need not be true. You can have a mean of 7 without any patient actually losing exactly 7 lbs. Example : 3,5,9,11.

f) Statement a) is true. So this is false.

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