GED Math : Mean

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #1 : Mean

Find the mean of the following numbers:
\(\displaystyle \small 29, 40, 40, 20, 11\)

Possible Answers:

\(\displaystyle \small 22\)

\(\displaystyle \small 29\)

\(\displaystyle \small 40\)

\(\displaystyle \small 28\)

Correct answer:

\(\displaystyle \small 28\)

Explanation:

\(\displaystyle \small mean=\frac{sum\ of\ all\ values}{number\ of\ values}\)

\(\displaystyle \small mean=\frac{29+40+40+20+11}{5}=\frac{140}{5}=28\)

Example Question #2 : Mean

Find the mean of the set of numbers below:

\(\displaystyle 18, 19, 20, 20, 22, 22, 23, 24\)

Possible Answers:

\(\displaystyle 24\)

\(\displaystyle 21\)

\(\displaystyle 20\)

\(\displaystyle 22\)

\(\displaystyle 18\)

Correct answer:

\(\displaystyle 21\)

Explanation:

\(\displaystyle \textup{The mean, or average, of a set of values }= \frac{\textup{sum of the values}}{\textup{number of values}}\)

In this list, \(\displaystyle \frac{\textup{sum of the values}}{\textup{number of values}}=\frac{18+19+20+20+22+22+23+24}{8}=21\)

Example Question #3 : Mean

Given the data set \(\displaystyle \left \{ 5, 6, 7, 8, 8, 9, 10, 11\right \}\), which of the following quantities are equal to each other/one another?

I: The mean

II: The median

III: The mode

Possible Answers:

I and III only

II and III only

I, II, and III

I and II only

Correct answer:

I, II, and III

Explanation:

The mean of a data set is the sum of its elements divided by the number of elements, which here is 8:

\(\displaystyle \frac{5+6+7+8+8+9+10+11}{8} = \frac{64}{8} = 8\)

The median of a data set with an even number of elements is the mean of the middle two values when the set is arranged in ascending order; both of the middle elements are 8, so the median is 8.

The mode of a data set is the most frequently occurring element. Here, only 8 appears twice, so it is the mode.

All three are equal.

Example Question #60 : Calculations

Veronica scored a 75 and a 71 on her first two exams. To raise her mean score to an 80, what grade does she need to earn on her third test?

Possible Answers:

90

94

85

73

80

Correct answer:

94

Explanation:

The mean score is the sum of all scores divided by the number of scores.

First, find the sum of all three test scores, then divide by the number of tests, 3.

\(\displaystyle Average = \frac{Score 1 + Score 2 + Score 3}{Number\ of\ Scores}\)

If Veronica wants her average to be 80, the equation becomes:

\(\displaystyle 80 = \frac{75 + 71 + x}{3}\)

We need to solve for \(\displaystyle x\).

First, multiply both sides of the equation by 3:

\(\displaystyle 240= 75 + 71 + x\)

\(\displaystyle 240 = 146 + x\)

Subtract 146 from both sides:

\(\displaystyle 94 = x\)

Veronica must score a 94 on her third test in order to bring her mean score to 80.

Example Question #61 : Calculations

Veronica went to the mall and bought several small gifts for her sister's birthday. The prices of the items were the following:

$8, $10, $6, $3, $7, $10, $2, $5, $3

What is the mean price?

Possible Answers:

$5

$6

$8

$3

$10

Correct answer:

$6

Explanation:

The mean of a set is the sum of all elements divided by the number of elements in the set:

\(\displaystyle Mean = \frac{total\ sum}{\#\ of\ elements}\)

\(\displaystyle Mean = \frac{8+10+6+3+7+10+2+5+3}{9}= \frac{54}{9} = 6\)

The mean is $6.

Example Question #62 : Calculations

On the first two tests of the year, James scored 100 and 70, respectively. He then scored a 96 on his third test. There is just one test remaining, and James wants to finish the semester with a 90 average. What score does he need to receive on the fourth test of the semester to finish with a mean score of 90?

Possible Answers:

94

92

90

99

100

Correct answer:

94

Explanation:

The mean in a data set of scores is the sum of all scores divided by the number of scores:

\(\displaystyle Mean = \frac{Sum\ of\ Scores}{\#\ of\ Scores}\)

Call the fourth test score \(\displaystyle x\). Plug in what we know and solve for \(\displaystyle x\):

\(\displaystyle 90= \frac{100+70+96+x}{4} = \frac{266+x}{4}\)

Multiply both sides by 4:

\(\displaystyle 360= 266 + x\)

Then, subtract 266 from both sides:.

\(\displaystyle 94 = x\)

To finish with a mean of 90, James must score a 94 on his fourth test.

 

Example Question #61 : Statistics

Calculate the mean of the following numbers:

\(\displaystyle 72, 143, 68, 171, 91\)

Possible Answers:

\(\displaystyle 91\)

\(\displaystyle 92\)

\(\displaystyle 75\)

\(\displaystyle 109\)

Correct answer:

\(\displaystyle 109\)

Explanation:

\(\displaystyle mean=\frac{\textup{sum of the elements}}{\textup{\# of elements}}=\frac{72+143+68+171+91}{5}=\frac{545}{5}=109\)

Example Question #64 : Calculations

John would like to have a 90 average for math for this semester. John received a 78, 89, 100 on three of his tests. What is the lowest grade he could receive on his last test in order for him to get a 90 average for the semester?

Possible Answers:

\(\displaystyle 90\)

\(\displaystyle 92\)

\(\displaystyle 83\)

\(\displaystyle 93\)

Correct answer:

\(\displaystyle 93\)

Explanation:

In order for John to maintain a 90 average for the marking period, his total for four tests must be 360.

\(\displaystyle \frac{360}{4} = 90\) or  \(\displaystyle 90 \times 4 = 360\)

If you add up the scores that he already received, he already has 267 points.

\(\displaystyle 78+ 89 + 100 = 267\)

If you take the total of 267, which is the total amount of points for the three tests already taken and subtract it from the 360 points which is the total amount of points needed for a 90 average, he would need to get a 93 on his last test.

\(\displaystyle 360 - 267 = 93\)

Example Question #4 : Mean

Determine the mean of the numbers:  \(\displaystyle [5,-9,14,1]\)

Possible Answers:

\(\displaystyle 14\)

\(\displaystyle \frac{1}{4}\)

\(\displaystyle \frac{29}{4}\)

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

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

Correct answer:

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

Explanation:

The mean is the average of all the numbers in the set of data.

Add the numbers together and divide the sum by 4.

\(\displaystyle \frac{5+(-9)+14+1}{4} = \frac{11}{4}\)

The answer is:  \(\displaystyle \frac{11}{4}\)

Example Question #62 : Statistics

Determine the mean of the numbers:  \(\displaystyle [3,-8,26,19]\)

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 10\)

\(\displaystyle 16\)

\(\displaystyle 12\)

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

Correct answer:

\(\displaystyle 10\)

Explanation:

The mean is the average of all the number ins the data set.

Add all the numbers and divide the sum by four.

\(\displaystyle \frac{3+(-8)+26+19}{4} = \frac{40}{4}\)

The answer is:  \(\displaystyle 10\)

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