To find the average of a set of numbers, add up the individual values and divide by the total number of values you have. 

For the test scores, we can set up the following equation with x being the score on the fourth test:

\(\displaystyle \frac{88+78+95+x}{4}=90\)

Now, solve for x

\(\displaystyle 88+78+95+x=360\)

\(\displaystyle 261+x=360\)

\(\displaystyle x=99\)

To find the mean of a set of numbers, you must add them all and then divide their sum by the number of total members of the set. 

\(\displaystyle 1+1+1+2+4+5+5+7+8+12=46\) and there are \(\displaystyle 10\) numbers in the set, so we divide \(\displaystyle 46\) by \(\displaystyle 10\),

\(\displaystyle \frac{1+1+1+2+4+5+5+7+8+12}{10}=\frac{46}{10}\)

giving us a mean of \(\displaystyle 4.6\).

The mean of a set of numbers is the same as its average. 

\(\displaystyle \text{Mean}=\text{Average}=\frac{\text{Sum of all the numbers}}{\text{Total number of individual items}}\)

So then, to find the mean weight for the puppies,

\(\displaystyle \text{Mean}=\frac{657+789+456+554+635+446}{6}=589.5\)

To find the average (also known as the mean), we use the following formula:

\(\displaystyle \text{Average}=\frac{\text{Sum of all given numbers}}{\text{The amount of numbers we have}}\)

So, for the numbers that are given in the question, we can set up this equation:

\(\displaystyle \text{Average}=\frac{14.51+11.21+9.53+17.56+8.29}{5}\)

\(\displaystyle \text{Average}=\frac{61.1}{5}=12.22\)

To find Judy's overall grade, you must find the mean of all five test scores.

Add together all five scores:

\(\displaystyle 87+91+79+88+90=435\)

Then divide the sum by the total number of scores:

\(\displaystyle 435\div5=87\)

\(\displaystyle 87\) is Judy's overall score in the class.

To find the mean, you must add all of the numbers together and divide by the amount of numbers. In this case there are four numbers so, we must deivide the total sum by 4.

\(\displaystyle \frac{22+44+134+200}{4}=\frac{400}{4}= 100\)

First, calculate the sum of all of the numbers.

\(\displaystyle \small 11+13+16+13+14+19+13+13=112\)

Next, divide by the total number.

\(\displaystyle \small \frac{112}{8}=14\)

We can treat this as if the entire class had exactly 86% as their average, so the new average is:

\(\displaystyle \frac{(86\cdot 15)+100}{16}=86.875\)

To find the mean you add all of the numbers together and divide it by the amount of numbers. In this case there are six numbers so \(\displaystyle \frac{(88+99+31+47+68+27)}{6}=\frac{360}{6}\)

The answer is \(\displaystyle 60\).

To find mean, we add up the values in a set and divide by the number of terms in that set. We begin this problem with the knowledge that the mean of the first set is 20. Since that set contains five numbers, we know that its total sum must be 100 (since 100 divided by 5 is 20).

 \(\displaystyle 27+11+14+23 = 75\)

so \(\displaystyle x\) must be 25.

Now, the only step left is to find the mean of \(\displaystyle \left \{ 25,50,11,8,31\right \}\).

These values add up to 125, and when we divide by 5, we are left with a final answer of 25.