An investment company advertised that last year its clients, on average, made a
ID: 3379954 • Letter: A
Question
An investment company advertised that last year its clients, on average, made a profit of 9%.
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, the number of their clients who made a profit of 9% or less was equal to the number of their clients who made a profit of 9% or more.
Last year all of their clients made a profit of at least 9%.
This year some of their clients will make a profit of at least 9%.
Last year at least one of their clients made a profit of less than 14%.
None of the above statements is true.
An investment company advertised that last year its clients, on average, made a profit of 9%.
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.
Explanation / Answer
Last year at least one of their clients made a profit of exactly 9%. [FALSE, the mean may not be even present in the data set.]
Last year, the number of their clients who made a profit of 9% or less was equal to the number of their clients who made a profit of 9% or more. [FALSE. If the distribution is not perfectly symmetric, this is already false.]
Last year all of their clients made a profit of at least 9%. [FALSE.]
This year some of their clients will make a profit of at least 9%. [FALSE. We don't know what's going to happen next year for sure.]
Last year at least one of their clients made a profit of less than 14%. [TRUE. The mean is 9%, so someone must have gottn a profit less than 14%.]
Thus, only this last statement is true.
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