To find the mean, or average, of a set of numbers, you first add all of the numbers together:

$\displaystyle 32+23+46+52+37=190$.

Then, you divide the sum by the total number of numbers, which in this set is 5 (i.e., there are 5 numbers in this set):

$\displaystyle 190\div5=38$.

38 is the mean, or average, of this set of numbers.

To calculate the average score, you must take the sum of Reese's scores and divide it by the number of tests he took (4). To get an average of 80, the sum of Reese's scores must be 320.

$\displaystyle (80*4=320)$

The sum of his first three test scores is 235.

$\displaystyle (73+79+83=235)$

Thus, Reese must earn a score of 85 on his fourth test

$\displaystyle (320-235=85)$

First, calculate the mean. Sum the values and divide by the total number of values:

$\displaystyle \frac{42+51+62+47+38+50+54+44}{8}=\frac{388}{8}=48.5$

Next, determine the median. Reorder the values in ascending order:

38, 42, 44, 47, 50, 51, 54, 62

The median is the middle number. In this case, there is no "middle" number because we have an even number of values. Therefore, both 47 and 50 are the "middle". Average these numbers:

$\displaystyle \frac{47+50}{2}=48.5$

Therefore, 48.5 represents both the mean and median.

The mean is the average. The mean can be found by taking the sum of all the numbers (150 + 88 + 141 + 110 + 79 = 568) and then dividing the sum by how many numbers there are (5).

$\displaystyle mean=\frac{150+88+141+110+79}{5}=\frac{568}{5}=113\frac{3}{5}$

Our answer is 113 3/5, which can be written as a decimal.

$\displaystyle \frac{3}{5}*\frac{2}{2}=\frac{6}{10}=0.6$

Therefore 113 3/5 is equivalent to 113.6, which is our answer.

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

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

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

Multiply both sides of the equation by 5.

$\displaystyle 352+x=450$

Subtract 352 from both sides of equation.

$\displaystyle x=98$

Let $\displaystyle y = 6x + 3$.

We know the mean is 8, and there are five values in the set, including the unknown $\displaystyle y$.

$\displaystyle mean=\frac{10+5+12+y+4}{5}=8$

$\displaystyle \left ( 10+5+12+y+4 )= \left ( 8* 5\right )$

Simplify.

$\displaystyle 31+y = 40$

$\displaystyle y = 9$

Plug back into equation at top.

$\displaystyle y = 6x + 3$

$\displaystyle 6x+3 = 9$

$\displaystyle 6x =6$

$\displaystyle x=1$

If the average of $\displaystyle 3$ numbers is $\displaystyle 2$, then the sum is $\displaystyle 6$.

We also know the average of $\displaystyle 4$ numbers is $\displaystyle 3$. We can set-up an equation. 

$\displaystyle \frac{6+x}{4}=3$.

The expression in the numerator represents the sum. By cross-multiplying, we get 

$\displaystyle 6+x=12$ or $\displaystyle x=6$ as the final answer. 

To find the average of all the numbers, we need to find the sums from each average. Since the average of $\displaystyle 3$ numbers is $\displaystyle 6$, that means the sum is $\displaystyle 18$.

The average of $\displaystyle 5$ numbers is $\displaystyle 7$ means the sum is $\displaystyle 35$.

Then, the total sum is $\displaystyle 53$ which is the sum of all the numbers.

So to find average, we do $\displaystyle 53$ divided by $\displaystyle 8$ to get $\displaystyle 6.625$. 

The mean is the same as the average. To find the mean, use the following formula:

$\displaystyle \text{Mean}=\frac{\text{Sum of all values}}{\text{Number of values}}$

$\displaystyle \text{Mean}=\frac{45+98+100+132+15}{5}$

$\displaystyle \text{Mean}=\frac{390}{5}$

$\displaystyle \text{Mean}=78$

The mean is the same as the average. To find the mean, use the following formula:

$\displaystyle \text{Mean}=\frac{\text{Sum of all values}}{\text{Number of values}}$

$\displaystyle \text{Mean}=\frac{(-98)+(-52)+(-15)+23}{4}$

$\displaystyle \text{Mean}=\frac{(-165)+23}{4}$

$\displaystyle \text{Mean}=\frac{(-142)}{4}$

$\displaystyle \text{Mean}=-35.5$