GED Math : GED Math

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #21 : Median

Determine the median of the numbers:  \(\displaystyle [-5,-3,6,-9]\)

Possible Answers:

\(\displaystyle \frac{3}{2}\)

\(\displaystyle \frac{9}{2}\)

\(\displaystyle -4\) 

\(\displaystyle -\frac{11}{4}\)

\(\displaystyle \textup{There is no median.}\)

Correct answer:

\(\displaystyle -4\) 

Explanation:

Rearrange the numbers from least to greatest.

\(\displaystyle [-5,-3,6,-9] \rightarrow [ -9,-5,-3,6]\)

Since there is an even amount of numbers the median is the average of the central two numbers in the data set.

\(\displaystyle \frac{-5+(-3)}{2} = \frac{-8}{2}\)

The answer is:  \(\displaystyle -4\)

Example Question #22 : Median

Timothy received the following scores for four math tests: \(\displaystyle 87, 88, 90, 85\). In order to get on the honor roll, Timothy must have an average of \(\displaystyle 90\) in his math class. He has one last test coming up. What must he score on the last test in order to make the honor roll?

Possible Answers:

\(\displaystyle 98\)

\(\displaystyle 100\)

\(\displaystyle 95\)

\(\displaystyle 92\)

Correct answer:

\(\displaystyle 100\)

Explanation:

Recall how to find the average of a set of numbers:

\(\displaystyle \text{Average}=\frac{\text{Sum of Terms}}{\text{Number of terms}}\)

Since we have a total of \(\displaystyle 5\) tests, we can write the following equation by using the information given by the question:

\(\displaystyle 90=\frac{87+88+90+85+x}{5}\),

where \(\displaystyle x\) is the score Timothy must earn on his final test.

Now, solve for \(\displaystyle x\).

\(\displaystyle 350+x=450\)

\(\displaystyle x=100\)

Example Question #1941 : Ged Math

Determine the median:  \(\displaystyle [-3,-1,-5,1,9]\)

Possible Answers:

\(\displaystyle -3\)

\(\displaystyle 3\)

\(\displaystyle 9\)

\(\displaystyle -1\)

\(\displaystyle \frac{1}{5}\)

Correct answer:

\(\displaystyle -1\)

Explanation:

Reorder the numbers from least to greatest.

\(\displaystyle [-3,-1,-5,1,9] \to [-5,-3,-1,1,9]\)

Since there is an odd amount of numbers, the median is the central number for all the numbers of the ordered set.

The answer is:  \(\displaystyle -1\)

Example Question #1942 : Ged Math

Determine the median of the numbers:  \(\displaystyle [-2,-3,6,9]\)

Possible Answers:

\(\displaystyle \frac{3}{2}\)

\(\displaystyle 2\)

\(\displaystyle \frac{5}{2}\)

\(\displaystyle \frac{4}{3}\)

\(\displaystyle \textup{There is no median.}\)

Correct answer:

\(\displaystyle 2\)

Explanation:

Rearrange the numbers from least to greatest.

\(\displaystyle [-2,-3,6,9] \rightarrow [ -3,-2,6,9]\)

The median is the average of the central two numbers.

\(\displaystyle \frac{-2+6}{2} = \frac{4}{2}\)

The answer is:  \(\displaystyle 2\)

Example Question #25 : Median

Find the median of the following data set:

\(\displaystyle 14,96,33,59,63,14,44,58,57,12,9\)

Possible Answers:

\(\displaystyle 14\)

\(\displaystyle 44\)

\(\displaystyle 41.7\)

\(\displaystyle 87\)

Correct answer:

\(\displaystyle 44\)

Explanation:

Find the median of the following data set:

\(\displaystyle 14,96,33,59,63,14,44,58,57,12,9\)

To find the median, let's first put our terms in increasing order:

\(\displaystyle 14,96,33,59,63,14,44,58,57,12,9\)

Becomes:

\(\displaystyle 9,12,14,14,33,44,57,58,59,63,96\)

Now, our median is simply the middle term. It is the term which has exactly 50% of the rest of the terms to either side of it.

\(\displaystyle 9,12,14,14,33,{\color{Blue} 44},57,58,59,63,96\)

In this case, it must be 44.

Example Question #122 : Calculations

Find the median of the following data set:

\(\displaystyle 44,67,234,989,33,45,64,44,23,34,11\)

Possible Answers:

\(\displaystyle 144\)

\(\displaystyle 34\)

\(\displaystyle 44\)

\(\displaystyle 45\)

Correct answer:

\(\displaystyle 44\)

Explanation:

Find the median of the following data set:

\(\displaystyle 44,67,234,989,33,45,64,44,23,34,11\)

Let's begin by putting our numbers in increasing order:

\(\displaystyle 11,23,33,34,44,44,45,64,67,234,989\)

Next, identify the median by finding the middle value.

\(\displaystyle 11,23,33,34,44,{\color{Green} 44},45,64,67,234,989\)

In this case, it is 44, because 44 is the 6th term in our series, making it the middle value.

Example Question #123 : Calculations

Find the median of the following data set:

\(\displaystyle 654,767,176,458,654,229,555,144,343,767,654\)

Possible Answers:

\(\displaystyle 555\)

\(\displaystyle 431\)

\(\displaystyle 654\)

\(\displaystyle 767\)

Correct answer:

\(\displaystyle 555\)

Explanation:

Find the median of the following data set:

\(\displaystyle 654,767,176,458,654,229,555,144,343,767,654\)

To find the median, first place your terms in increasing order

\(\displaystyle 144,176,229,343,458,555,654,654,654,767,767\)

Next, ID the median by simply choosing the middle term.

\(\displaystyle 144,176,229,343,458, {\color{Blue} 555},654,654,654,767,767\)

So, our answer is 555

Example Question #1943 : Ged Math

Give the median of the data set:

\(\displaystyle \left \{ 6, 3, 2, 1, 5, 1, 9, 2, 1 \right \}\)

Possible Answers:

\(\displaystyle 5\)

\(\displaystyle 2\)

\(\displaystyle 9\)

\(\displaystyle 1\)

Correct answer:

\(\displaystyle 2\)

Explanation:

If the elements of a data set with nine elements - an odd number - are arranged in ascending order, the median of the set is the element that appears in the exact center. The data set, arranged, is

\(\displaystyle \left \{ 1,1,1,2, \textbf{{\color{Red} 2}}, 3, 5, 6, 9 \right \}\)

The element in the center is 2, which is the median.

Example Question #125 : Calculations

What is the median for this set of data? 

\(\displaystyle 1\)\(\displaystyle 5\)\(\displaystyle 9\)\(\displaystyle 13\)\(\displaystyle 17\)

Possible Answers:

\(\displaystyle 1\)

\(\displaystyle 5\)

\(\displaystyle 17\)

\(\displaystyle 9\)

\(\displaystyle 13\)

Correct answer:

\(\displaystyle 9\)

Explanation:

The median is the middle number of a set after it has been ordered from least to greatest. We have \(\displaystyle 5\) numbers in this set, so our middle number should have \(\displaystyle 2\) numbers on both the left and right side of it in order to be in the middle.

\(\displaystyle 9\) is the only number that has \(\displaystyle 2\) numbers on the left and right side of it, so this must be our middle.

Our answer is \(\displaystyle 9\).

Example Question #131 : Statistics

What is the mean of this set? 

\(\displaystyle 2\)\(\displaystyle 4\)\(\displaystyle 6\)\(\displaystyle 8\)

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 2\)

\(\displaystyle 5\)

\(\displaystyle 4\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle 5\)

Explanation:

In order to find the median, we must first make sure our set is ordered from least to greatest, then take the middle number. We can see that it is, as \(\displaystyle 2\), the smallest number, is first and \(\displaystyle 8\), the largest number, is last.

Here we can see that we have \(\displaystyle 4\) numbers in this set, so we don't have a number that sits between an equal amount of numbers on either side. Our two most middle numbers are \(\displaystyle 4\) and \(\displaystyle 6\).

Choosing one will not give us the right answer, so in order to find the median, we must add these two together and divide by \(\displaystyle 2\), because that is how many numbers we are adding together.

\(\displaystyle \frac{4+6}{2}=5\)

\(\displaystyle 5\) is our median because it is the number that sits between \(\displaystyle 4\) and \(\displaystyle 6\).

Our answer is \(\displaystyle 5\).

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