An investment company advertised that last year its clients, on average, made 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 at least one of their clients made a profit of exactly | 9% Last year, the number of their clients who made a profit of 9% or more was equal to the number of their clients who made a profit of 9% or less Last year some of their clients made a profit of less than 14% Two years ago some of their clients made a profit of at least 19% Last year at least one of their clients made a profit of 9% or more. None of the above statements is true.

Explanation / Answer

For mean profit of 9%, it is not necessary that atleast one of clients made exactly 9%. For example, for 2 clients, let the profit of two clients are 10% and 8%. The average of profit is 9% but none of the client's profit is 9%. So, the first option is not correct.

Let there be 3 clients, let the profit of three clients are 8%, 11% and 8%. The average of profit is 9% but number of clients who made profit of 9% or more is 1 and clients who made profit of 9% or less is 2 and they are not equal. So, the second option is not correct.

For average of 9%, atleast some of the clients should made a profit of less than 14%, else the average profit will be greater than 14%. So, third option is correct.

The claim is only for last year. So, the fourth option is not correct.

For average of 9%, atleast one of the clients should made a profit of 9% or more, else the average profit will be less than 9%. So, fifth option is correct.

So, the correct options are,

Last year some of their clients made a profit of less than 14%

Last year at least one of their clients made a profit of 9% or more.

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