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Flashcards: Working with Statistics

If the set {10, 5, 9, x} has a median of 7, which of the following could not be a possible value of x?

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Flashcards: Working with Statistics

If the set {10, 5, 9, x} has a median of 7, which of the following could not be a possible value of x?

Your answer:

Correct answer:

Explanation:

When you are asked to find the median, your first step should always to be to check to see if the numbers are in ascending order. If they aren’t, your next step should be to put them in order. If you have variables, remember that without any additional information about the set, you don’t know where in the set the variable should be placed, so just put it to one side or the other until you integrate additional information. For this set, you should rearrange them to get:

{5, 9, 10, x}

You are also told that the median to this set is 7. Since the set has an even number of terms, that means that 7 must be the average of the two middle numbers. And since 7 is halfway between 5 and 9, those two numbers must be the two middle numbers. You can therefore rewrite the set in ascending order as

{x, 5, 9, 10}

It should be obvious that x could be 1, 3, or 4. It could also be 5, since that would not change the median at all since the two middle numbers would still be 5 and 9. However, it could not be 7, since the average of 7 and 9 is 8, not 7.

Flashcards: Working with Statistics

Over five different years, the total rainfall in Brooks County was, in ascending order, 15 inches, 24 inches, inches, 45 inches, and 60 inches. If the average annual rainfall was equal to the median annual rainfall for those five years, what was the average rainfall?

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Flashcards: Working with Statistics

Your answer:

Correct answer:

Explanation:

Since the five values are given in ascending order, you know that the median - which is defined as the middle value for an odd-numbered set - is the third value, x. For the median to then equal the mean, you'll calculate the mean. The mean is the sum of the values divided by the number of values, or here: $\frac{15+24+x+45+60}{5}$ . So you know that:

Median = Mean

x=\frac{15+24+x+45+60}{5}

Now you can solve for x. To eliminate the denominator, multiply both sides by 5 to get:

Then combine like terms:

Then subtract from both sides:

Then you can solve for x=36 .

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Flashcards: Working with Statistics

Flashcards: Working with Statistics

Flashcards: Working with Statistics

Flashcards: Working with Statistics

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All SAT Mathematics Resources

Flashcards: Working with Statistics

Flashcards: Working with Statistics

Flashcards: Working with Statistics

Flashcards: Working with Statistics

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