To find the mean of a certain set of numbers we need to add all enteries together and then divide by how many numbers you have.

In our case we do:

\(\displaystyle \frac{87+92+77+90}{4}\)

\(\displaystyle \frac{346}{4}\)

\(\displaystyle 86.5\)

For this question we need to set up an equation to find the mean, set it equal to our desired mean of 92 and solve for our missing test value.

\(\displaystyle \frac{93+88+87+95+x}{5}=92\)

From here we perform algebraic procedures to simplify the equation

\(\displaystyle \frac{363+x}{5}=92\)

\(\displaystyle 363+x=460\)

\(\displaystyle x=97\)

To solve this problem we use the equation to find the mean. We add all entries and then divide by the number of entries we have. It is as follows:

\(\displaystyle \frac{10+9+5}{3}=\frac{24}{3}\)

\(\displaystyle \frac{24}{3}=8\)

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

\(\displaystyle \text{Mean}=\frac{\text{Sum of all values}}{\text{Number of Values}}\)

\(\displaystyle \text{Mean}=\frac{100+90+67+89+78}{5}=84.8\)

First, write out the individual values found within this stem and leaf plot to figure out how many values there are.

\(\displaystyle \text{Values}: 20, 21, 24, 24, 30, 31, 31, 32, 32, 35, 37, 41, 45\)

Now, finding the mean is the same as finding the average. Recall how to find the average:

\(\displaystyle \text{Mean/Average}=\frac{\text{Sum of all values}}{\text{Number of values}}\)

Thus, the mean number of baseball cards owned is found by the following:

\(\displaystyle \text{Mean}=\frac{20+21+24+24+30+31+31+32+32+35+37+41+45}{13}=31\)

Recall how to find the average of a set of numbers:

\(\displaystyle \text{Mean/Average}=\frac{\text{Sum of all values}}{\text{Number of values}}\)

Now, let \(\displaystyle x\) be the score Michael needs on his last test in order to have a test average of \(\displaystyle 80\).

\(\displaystyle 80=\frac{65+90+78+67+x}{5}\)

Now, solve for \(\displaystyle x\).

\(\displaystyle 300+x=400\)

\(\displaystyle x=100\)

First, figure out the temperatures.

May: \(\displaystyle 69\)

June:\(\displaystyle 78\)

July: \(\displaystyle 88\)

August: \(\displaystyle 86\)

September:\(\displaystyle 79\)

Now, recall how to find the mean of a set of numbers:

\(\displaystyle \text{Mean/Average}=\frac{\text{Sum of all values}}{\text{Number of values}}\)

\(\displaystyle \text{Mean}=\frac{69+78+88+86+79}{5}=80\)

Recall how to find the mean:

\(\displaystyle \text{Mean/Average}=\frac{\text{Sum of all values}}{\text{Number of values}}\)

\(\displaystyle \frac{x+(x-1)+(x+7)+(x+10)}{4}=9\)

\(\displaystyle 4x+16=36\)

\(\displaystyle 4x=20\)

\(\displaystyle x=5\)

Recall how to find the mean:

\(\displaystyle \text{Mean/Average}=\frac{\text{Sum of all values}}{\text{Number of values}}\)

\(\displaystyle 30=\frac{(x)+(x+11)+(x-4)+(x-11)}{4}\)

\(\displaystyle 4x-4=120\)

\(\displaystyle 4x=124\)

\(\displaystyle x=31\)

Now, because the question asks you to find the smallest number, you need to find the value of \(\displaystyle x-11\).

\(\displaystyle x-11=31-11=20\)

Recall how to find the mean:

\(\displaystyle \text{Mean/Average}=\frac{\text{Sum of all values}}{\text{Number of values}}\)

\(\displaystyle 10=\frac{x+(x-1)+(x-15)+(x+20)}{4}\)

\(\displaystyle 4x+4=40\)

\(\displaystyle 4x=36\)

\(\displaystyle x=9\)

Now, because the question asks you to find the largest number, we need to find the value of \(\displaystyle x+20\).

\(\displaystyle x+20=9+20=29\)