GED Math : Mean

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #1881 : Ged Math

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

\(\displaystyle 78, 95, 84, 81, 93, 88, 83\)

Find the mean.

Possible Answers:

\(\displaystyle 81\)

\(\displaystyle 88\)

\(\displaystyle 90\)

\(\displaystyle 86\)

\(\displaystyle 84\)

Correct answer:

\(\displaystyle 86\)

Explanation:

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

\(\displaystyle \text{mean} = \frac{\text{sum of numbers within set}}{\text{number of numbers within set}}\)

So, given the set

\(\displaystyle 78, 95, 84, 81, 93, 88, 83\)

we can calculate the following:

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

\(\displaystyle \text{sum of numbers within set} = 602\)

We can also calculate the following:

\(\displaystyle \text{number of numbers within set} = 7\)

because there are 7 numbers in the data set.

So, we can substitute. We get

\(\displaystyle \text{mean} = \frac{602}{7}\)

\(\displaystyle \text{mean} = 86\)

Therefore, the mean of the data set is 86.

Example Question #1882 : Ged Math

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

\(\displaystyle 77, 75, 88, 81, 93, 86, 80, 92, 84\)

Find the mean score.

Possible Answers:

\(\displaystyle 81\)

\(\displaystyle 88\)

\(\displaystyle 77\)

\(\displaystyle 84\)

\(\displaystyle 85\)

Correct answer:

\(\displaystyle 84\)

Explanation:

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

\(\displaystyle \text{mean} = \frac{\text{sum of numbers within set}}{\text{number of numbers within set}}\)

Now, given the set

\(\displaystyle 77, 75, 88, 81, 93, 86, 80, 92, 84\)

We can calculate the following:

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

\(\displaystyle \text{sum of numbers within set} = 756\)

We can also calculate the following:

\(\displaystyle \text{number of numbers within set} = 9\)

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

So, we can substitute. We get

\(\displaystyle \text{mean} = \frac{756}{9}\)

\(\displaystyle \text{mean} = 84\)

Therefore, the mean score is 84.

Example Question #61 : Statistics

Determine the mean of the numbers:  \(\displaystyle [-1,-2,5,8]\)

Possible Answers:

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

\(\displaystyle \frac{15}{4}\)

\(\displaystyle 2\)

\(\displaystyle 0\)

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

Correct answer:

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

Explanation:

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

Add all the numbers and divide the total by four.

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

Reduce the fraction.

The mean is:  \(\displaystyle \frac{5}{2}\)

Example Question #62 : Statistics

Determine the mean of the numbers:  \(\displaystyle [-5,-6,9,14]\)

Possible Answers:

\(\displaystyle 2\)

\(\displaystyle 23\)

\(\displaystyle 5\)

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

\(\displaystyle 3\)

Correct answer:

\(\displaystyle 3\)

Explanation:

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

Add the numbers and divide the quantity by four.

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

The mean is:  \(\displaystyle 3\)

Example Question #71 : Statistics

Determine the mean of the numbers:  \(\displaystyle [-9,-6,12,13]\)

Possible Answers:

\(\displaystyle 3\)

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

\(\displaystyle \frac{15}{4}\)

\(\displaystyle 0\)

\(\displaystyle \frac{25}{4}\)

Correct answer:

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

Explanation:

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

Sum all the numbers and divide the quantity by 4.

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

The answer is:  \(\displaystyle \frac{5}{2}\)

Example Question #1891 : Ged Math

There are nine people in an elevator.  They have an average weight of \(\displaystyle 157\) lbs.  Two more people enter the elevator.  They have an average weight of \(\displaystyle 177\) lbs.  What is the new average weight of the group in the elevator?  Round to the nearest hundredth of a pound.

Possible Answers:

\(\displaystyle 160.64\) lbs.

\(\displaystyle 158.21\) lbs.

\(\displaystyle 166.32\) lbs.

\(\displaystyle 167\) lbs.

\(\displaystyle 196.33\) lbs.

Correct answer:

\(\displaystyle 160.64\) lbs.

Explanation:

To figure out this problem, you must first calculate the total pounds in the elevator.

The first group is:

\(\displaystyle 9*157\) or \(\displaystyle 1413\) lbs.

The second group is:

\(\displaystyle 2*177\) or \(\displaystyle 354\) lbs.

Thus, the total amount is:

\(\displaystyle 354+1413=1767\)

Thus, the average weight in the elevator will be:

\(\displaystyle \frac{1767}{11}\) (Remember, there are now \(\displaystyle 11\) people in the elevator.)

This is \(\displaystyle 160.63636363636364\) or \(\displaystyle 160.64\) lbs.

Example Question #72 : Statistics

Determine the mean:  \(\displaystyle [1,5,9,11,24,26]\)

Possible Answers:

\(\displaystyle \frac{38}{5}\)

\(\displaystyle 10\)

\(\displaystyle 19\)

\(\displaystyle \frac{5}{3}\)

\(\displaystyle \frac{38}{3}\)

Correct answer:

\(\displaystyle \frac{38}{3}\)

Explanation:

Sum all the numbers and divide the quantity by 6.

\(\displaystyle \frac{(1+5+9+11+24+26)}{6} = \frac{76}{6}\)

Reduce this fraction.

The answer is:  \(\displaystyle \frac{38}{3}\)

Example Question #73 : Statistics

Evaluate the mean:  \(\displaystyle [2,8,10,-2,20]\)

Possible Answers:

\(\displaystyle \frac{38}{3}\)

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

\(\displaystyle 8\)

\(\displaystyle \frac{8}{5}\)

\(\displaystyle \frac{38}{5}\)

Correct answer:

\(\displaystyle \frac{38}{5}\)

Explanation:

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

Add all numbers and divide the total by five.

\(\displaystyle \frac{2+8+10+(-2)+20}{5} = \frac{38}{5}\)

The answer is:  \(\displaystyle \frac{38}{5}\)

Example Question #74 : Statistics

Find the mean of the numbers:  \(\displaystyle [8,9,-4,-3,15,2]\)

Possible Answers:

\(\displaystyle 4\)

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

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

\(\displaystyle \frac{9}{4}\)

\(\displaystyle \frac{41}{6}\)

Correct answer:

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

Explanation:

The mean is the average of all the numbers.

Add all the numbers and divide the sum by 6.

\(\displaystyle \frac{8+9+(-4)+(-3)+15+2}{6} = \frac{27}{6}\)

Reduce this fraction.

The answer is:  \(\displaystyle \frac{9}{2}\)

Example Question #75 : Statistics

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?

Possible Answers:

D

C

F

B

Correct answer:

C

Explanation:

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;

\(\displaystyle \frac{68+77+73 + 80}{4} = \frac{298}{4}= 74.5\)

\(\displaystyle 70 \le 74.5 < 80\),

so Charlie made a grade of "C".

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