Calculations - GED Math

Card 0 of 1030

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

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?

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

A penny is altered so that the odds are 5 to 4 against it coming up tails when tossed; a nickel is altered so that the odds are 4 to 3 against it coming up tails when tossed. If both coins are tossed, what are the odds of there being two heads or two tails?

Answer

5 to 4 odds in favor of heads is equal to a probability of $\frac{5}{5 + 4} = \frac{5}{9}$ , which is the probability that the penny will come up heads. The probability that the penny will come up tails is $1 - \frac{5}{9} = \frac{4}{9}$ .

Similarly, 4 to 3 odds in favor of heads is equal to a probability of $\frac{4}{4+3} = \frac{4}{7}$ , which is the probability that the nickel will come up heads. The probablity that the nickel will come up tails is $1 - \frac{4}{7} = \frac{3}{7}$ .

The outcomes of the tosses of the penny and the nickel are independent, so the probabilities can be multiplied.

The probability of the penny and the nickel both coming up heads is $\frac{5}{9} \times \frac{4}{7} = \frac{20}{63}$ .

The probability of the penny and the nickel both coming up tails is $\frac{4}{9} \times \frac{3}{7} = \frac{12}{63}$ .

The probabilities are added:

$\frac{20}{63}+ \frac{12}{63} = \frac{20 + 12}{63 }= \frac{32}{63}$

Since , this translates to 32 to 31 odds in favor of this event.

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Question

Given the data set $\left { 0, 5, 5, 5, 5, 10, 15, 20, 25 \right }$ , which of the following quantities are equal to each other/one another?

I: The mean

II: The median

III: The mode

Answer

The median of a data set with an odd number of elements is the middle value when the set is arranged in ascending order; the middle value of this nine-element set is the fifth value, 5.

The mode of a data set is the most frequently occurring element. Here, only 5 appears multiple times, so it is the mode.

The mean of a data set is the sum of its elements divided by the number of elements, which here is 9:

$\frac{0+5+5+5+5+10+15+20+25}{9}= \frac{90}{9} = 10$

The mean and the mode are equal, but the mean is different. The correct answer is "II and III only".

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Question

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

$8, $10, $6, $7, $10, $2, $5, $3, $4

What is the medianprice of the gifts?

Answer

To find the median, first reorder the prices in ascending order:

$2, $3, $4, $5, $6, $7, $8, $10, $10

The median is the middle number in a data set.

Here, the middle number in this set of nine prices is the 5th number, which is $6.

$2, $3, $4, $5, $6, $7, $8, $10, $10

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Question

Philip went to a family reunion this weekend and met his extended cousins, whose ages were the following:

10, 21, 7, 8, 19, 20, 8, 15, 17, and 13.

What is the medianage?

Answer

The median is the middlenumber in a data set.

To find the median, rearrange the numbers in ascending order and find the middle number:

Given: 10, 21, 7, 8, 19, 20, 8, 15, 17, 13.

In order: 7, 8, 8, 10, 13, 15, 17, 19, 20, 21.

Since the data set has 10 numbers, which is even, the median is the average of the two middle numbers. The two numbers in the middle of this data set are 13 and 15. Their average, or the number in between them, is 14.

Therefore the median age is 14.

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Question

How many modes does this data set:

$\left { 3,4,6,6,6,7,7,8,8,8,8,9,10,11\right }$

Answer

The mode of a data set is the element that occurs most frequently. If there is a tie between the frequencies of two (three, etc.) elements, the set has two (three, etc.) modes.

Here, though, only one element (8) appears four times, with no other element appearing more frequently. 8 is the only mode.

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Question

Give the mode of the data set:

$\left { 6, 3, 2, 1, 5, 1, 9, 2, 1 \right }$

Answer

The mode of a data set is the value that occurs the most frequently. If the data values are arranged in order, the set looks like this:

$\left { {\color{Red} \textbf{1,1,1},}2, 2, 3, 5, 6, 9 \right }$

1 occurs three times, more than any other element. This makes 1 the mode.

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Question

Calculate the mean of the following numbers:

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:
$\small 29, 40, 40, 20, 11$

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:

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?

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?

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?

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?

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:

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:

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.

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.

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:

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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