Homework Sourse40000 Assuming that average refers to the mean which of the
$40,000. 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 had a starting salary of more than
$40,000 was equal to the number of their clients who had a starting salary of less than $40,000.
Last year some of their clients had a starting salary of exactly $40,000.
Two years ago at least one of their clients had a starting salary of at least $40,000.
None of the above statements is true.
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Solution
A job placement agency advertised that last year its clients, on average, had a starting salary of $40,000.
This indicates that the mean of the starting salary was EXACTLY 40000 dollars.
This would indicate that there could have been some people who had a salary of exactly 40000.
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claim 1 :
Last year all of their clients had a starting salary of $40,000 or above
FALSE because some of them could have had less and some could have had more than 40000
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claim 2 :
Last year some of their clients had a starting salary of more than $37,000.
TRUE. This definitely has to be true cuz only if some have a salary more than 37000 can the mean be 40000
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claim 3 :
Last year, the number of their clients who had a starting salary of more than $40,000 was equal to the number of their clients who had a starting salary of less than $40,000.
FALSE. This need not have been true as we can have 3 people who have salaries close to but less than 40000 and we can have a person who has a salary much larger than 40000 and still have the mean to be exactly 40000.
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claim 4 :
Last year some of their clients had a starting salary of exactly $40,000.
FALSE. This need not be the case either because it is possible to have a bunch of salaries in and around 40000 and still ensure that the mean is 40000, for example salaries of 39999 and 40001 have a mean of exactly 40000 and neither value equals 40000.
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claim 5 :
Two years ago at least one of their clients had a starting salary of at least $40,000.
FALSE. Nothing can be said about the salary situation 2 yrs ago.
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So, there is only one correct claim ,i.e
\"Last year some of their clients had a starting salary of more than $37,000.\"
