Mean - GED Math

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Question

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

I: The mean

II: The median

III: The mode

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Answer

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

$\frac{5+6+7+8+8+9+10+11}{8} = \frac{64}{8} = 8$

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.

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Question

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

I: The mean

II: The median

III: The mode

Tap to reveal answer

Answer

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

$\frac{5+6+7+8+8+9+10+11}{8} = \frac{64}{8} = 8$

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.

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Question

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

I: The mean

II: The median

III: The mode

Tap to reveal answer

Answer

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

$\frac{5+6+7+8+8+9+10+11}{8} = \frac{64}{8} = 8$

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.

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Question

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

I: The mean

II: The median

III: The mode

Tap to reveal answer

Answer

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

$\frac{5+6+7+8+8+9+10+11}{8} = \frac{64}{8} = 8$

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.

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Question

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

I: The mean

II: The median

III: The mode

Tap to reveal answer

Answer

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

$\frac{5+6+7+8+8+9+10+11}{8} = \frac{64}{8} = 8$

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.

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Question

The grade a student earns for a course depends on the mean of the best four of the five tests he takes. The minimum mean score for each grade is as follows:

A: 90

B: 80

C: 70

D: 60

Charles earned 68, 50, 77, 73, and 80 on his five tests. What was his letter grade?

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Answer

Charlie's lowest score was a 50, so his grade was the mean of 68, 77, 73, and 80, which is the sum of the scores divided by the number of scores, 4;

$\frac{68+77+73 + 80}{4} = \frac{298}{4}= 74.5$

$70 \le 74.5 < 80$ ,

so Charlie made a grade of "C".

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Question

Calculate the mean of the following numbers:

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Answer

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

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Question

Find the mean of the following numbers:
$\small 29, 40, 40, 20, 11$

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Answer

$\small mean=\frac{sum\ of\ all\ values}{number\ of\ values}$

$\small mean=\frac{29+40+40+20+11}{5}=\frac{140}{5}=28$

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Question

Find the mean of the set of numbers below:

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Answer

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

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

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Question

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?

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Answer

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

$\frac{360}{4} = 90$ or $90 \times 4 = 360$

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

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.

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Question

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?

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Answer

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.

$Average = \frac{Score 1 + Score 2 + Score 3}{Number\ of\ Scores}$

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

$80 = \frac{75 + 71 + x}{3}$

We need to solve for .

First, multiply both sides of the equation by 3:

Subtract 146 from both sides:

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

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Question

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?

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Answer

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

$Mean = \frac{total\ sum}{#\ of\ elements}$

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

The mean is $6.

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Question

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?

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Answer

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

$Mean = \frac{Sum\ of\ Scores}{#\ of\ Scores}$

Call the fourth test score . Plug in what we know and solve for :

$90= \frac{100+70+96+x}{4} = \frac{266+x}{4}$

Multiply both sides by 4:

Then, subtract 266 from both sides:.

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

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Question

Determine the mean of the numbers:

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Answer

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

Add the numbers together and divide the sum by 4.

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

The answer is: $\frac{11}{4}$

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Question

Determine the mean of the numbers:

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Answer

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

Add all the numbers and divide the sum by four.

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

The answer is:

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Question

Use the following data set of test scores to answer the question:

Find the mean.

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Answer

To find the mean (or average), we will use the following formula:

$\text{mean} = \frac{\text{sum of numbers within set}}{\text{number of numbers within set}}$

So, given the set

we can calculate the following:

$\text{sum of numbers within set} = 78+95+84+81+93+88+83$

$\text{sum of numbers within set} = 602$

We can also calculate the following:

$\text{number of numbers within set} = 7$

because there are 7 numbers in the data set.

So, we can substitute. We get

$\text{mean} = \frac{602}{7}$

$\text{mean} = 86$

Therefore, the mean of the data set is 86.

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Question

A Science class took an exam. Here are the scores of 9 students:

Find the mean score.

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Answer

To find the mean, we will use the following formula:

$\text{mean} = \frac{\text{sum of numbers within set}}{\text{number of numbers within set}}$

Now, given the set

We can calculate the following:

$\text{sum of numbers within set} = 77+75+88+81+93+86+80+92+84$

$\text{sum of numbers within set} = 756$

We can also calculate the following:

$\text{number of numbers within set} = 9$

because if we count, we can see there are 9 numbers in the set.

So, we can substitute. We get

$\text{mean} = \frac{756}{9}$

$\text{mean} = 84$

Therefore, the mean score is 84.

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Question

Determine the mean of the numbers:

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Answer

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

Add all the numbers and divide the total by four.

$\frac{-1+(-2)+5+8}{4} = \frac{10}{4}$

Reduce the fraction.

The mean is: $\frac{5}{2}$

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Question

Determine the mean of the numbers:

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Answer

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

Add the numbers and divide the quantity by four.

$\frac{-5+(-6)+9+14}{4} = \frac{12}{4} = 3$

The mean is:

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Question

Determine the mean of the numbers:

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Answer

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

Sum all the numbers and divide the quantity by 4.

$\frac{-9+(-6)+12+13}{4} = \frac{10}{4} = \frac{5}{2}$

The answer is: $\frac{5}{2}$

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