Algebra - How to find mean

What is the mean of the following dataset? $[\frac{8}{3},\frac{1}{3},\frac{6}{3}]$

$\frac{5}{3}$

$\frac{1}{5}$

$\frac{3}{5}$

Explanation

To find the mean, add all the numbers and divide by the total amount of numbers in the dataset.

$\frac{\frac{8}{3}+\frac{1}{3}+\frac{6}{3}}{3}$

Add the numerator.

$\frac{8}{3}+\frac{1}{3}+\frac{6}{3} = \frac{15}{3}=5$

Divide this by the denominator.

The mean is: $\frac{5}{3}$

What is the mean of and ?

$-\frac{1}{4}$

$\frac{1}{4}$

$-\frac{1}{2}$

$\frac{1}{2}$

Explanation

In order to find the mean of a set of numbers, we divide the sum of the numbers by the amount of numbers in the set. Since we have numbers in the set, we can calculate the mean as the following:

$\frac{4+(-4)+6+(-7)}{4}$

$=\frac{6-7}{4}$

$=-\frac{1}{4}$

A class has a sum of test scores of . There are people in the class. What is the class average?

Cannot be determined

Explanation

Average is another way of describing mean. The mean represents the "central" value of a set of numbers. This is achieved by summing the numbers of a set and dividing it by the number of numbers in the set.

In this problem, the sum of all the scores is already provided. Because there are students, we can assume that is the sum of scores. Therefore, all we need to do is divide the sum by the number of scores.

$\frac{3871}{42}$

$=92.1667 \approx {\color{Blue} 92.2}$

What is the mean given the following set? $x=[\frac{1}{2}, \frac{1}{4}, \frac{1}{6}]$

$\frac{11}{36}$

$\frac{11}{12}$

$\frac{11}{4}$

$\frac{1}{4}$

$\frac{4}{11}$

Explanation

To find the mean, add all the numbers in the set and divide by the total numbers in the set.

Convert $\frac{1}{2}+\frac{1}{4}+\frac{1}{6}$ to a common denominator and then add to find the total.

$\frac{1}{2}+\frac{1}{4}+\frac{1}{6} = \frac{6}{12}+\frac{3}{12}+\frac{2}{12} = \frac{11}{12}$

Dividing this sum by three is the same as multiplying the sum by one third.

$\frac{11}{12} \div 3 = \frac{11}{12}\times \frac{1}{3} = \frac{11}{36}$

The average is $\frac{11}{36}$ .

Find the mean: 4 4 2 3 3 2 3 1 1 2 3 2 2 2 1 14 2

Explanation

The sum of every data point is 51. There are 17 data points. 51 divided by 17 is 3.

$\small 1,2,3,4,5,6,7,8,9,10,100$

Using the data above, find the mean.

$\small \frac{155}{11}$

$\small \frac{11}{155}$

$\small \frac{5}{11}$

$\small \frac{12}{5}$

$\small 5$

Explanation

To find the mean of the data set, all of the data values must be added together.

In this set provided,

$\small 1+2+3+4...+100 = 155$ .

The next step is to divide the sum of the data values by the amount of data values, $\small 155\div11$ .

Since the answer to this is a repeating decimal, leaving it in the form of a fraction would suffice. Remember, fractions can be read as division problems, thus division problems can be written as fractions.

So $\small 155\div 11$ is equivalent to $\small \frac{155}{11}$ .

Reginald has scores of {87, 79, 95, 91} on the first four exams in his Spanish class. What is the minimum score he must get on the fifth exam to get an A (90 or higher) for his final grade?

Explanation

To find the fifth score, we need to set the average of all of the scores equal to 90.

$\frac{(87+79+95+91+x)}{5}=90$

$\frac{(352+x)}{5}=90$

Multiply both sides of the equation by 5.

Subtract 352 from both sides of equation.

Mrs. Hooper's Algebra 1 test just completed their 10th test of the year. They were currently studying mean, so Mrs. Hooper gave them the list of scores in the class and asked them to find the mean. What should their answer be if the scores were as listed below?

Explanation

The mean means the average of all of the scores. You have to add up all of the scores and divide by the total. If you add up all scores you would get . You need to divide the total by , and the answer is .

$\frac{80+85+90+95+99+87+83+82+93+91+100+90+74+65+90}{15}$

If you round to the nearest, you would get as the mean score.

Refer to the following set of numbers:

What is the mean of the set?

Explanation

In order to find the mean of the set, we find its average. Do this by adding up all of the numbers in the set, then dividing that answer by the amount of numbers in the set.

$\frac{23+24+24+24+26+27+29+29+31+36}{10}=\frac{273}{10}=27.3$