To find the mean (or average) of a data set, you add all of the numbers within the set, then divide by how many numbers are in the data set.  In other words,

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

We will first find the sum.

\(\displaystyle \text{sum of numbers} = 8+ 4+ 5+ 10+ 3\)

\(\displaystyle \text{sum of numbers} = 30\)

Now, we will determine how many numbers are in the data set. 

\(\displaystyle \text{number of numbers} = 5\)

This is true, because the set contains 5 numbers.  

Now, we will substitute. 

\(\displaystyle \text{mean} = \frac{30}{5}\)

\(\displaystyle \text{mean} = 6\)

Therefore, the mean of the data set is \(\displaystyle 6\).

Find the mean of the following data set:

\(\displaystyle 16,27,45,27,87,99,127\)

To find the median, we need to add up all our terms and divide by the number of terms. This is the same process used to find the average of a group of numbers

\(\displaystyle 16+27+45+27+87+99+127=428\)

Because there are 7 terms in our series, we divide by 7

\(\displaystyle \frac{428}{7}=61.14286\approx61\)

So, we can say our answer is 61

To find the mean of a data set, we add all of the numbers within the set, then we divide that by the number of numbers within the set.  In other words, we will use this formula:

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

So, using the data set

\(\displaystyle 7, 4, 6, 7, 5, 7, 6\)

we will first find the sum of the numbers.  This means we will add the numbers.  So,

\(\displaystyle \text{sum of numbers} = 7+4+6+7+5+7+6\)

\(\displaystyle \text{sum of numbers} = 42\)

Now, we will find the number of numbers.  This just means that we will count and see how many numbers are in the set.  So, in the set

\(\displaystyle 7, 4, 6, 7, 5, 7, 6\)

we can see there are 7 numbers.  So,

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

Now, we can substitute into the formula.  We get

\(\displaystyle \text{mean} = \frac{42}{7}\)

\(\displaystyle \text{mean} = 6\)

Therefore, the mean is \(\displaystyle 6\).

To solve, first add all the numbers in the set:

\(\displaystyle 59+55+51+50+55=270\)

Then divide by the amount of numbers in the set:

\(\displaystyle 270\div 5=54\)

Answer: The mean is \(\displaystyle 54\).

What is the mean of the following data set?

\(\displaystyle 145,678,902,8902,145,33,34,147,678,902,333,92,145\)

First, find the sum of our terms:

\(\displaystyle 145+678+902+8902+145+33+34+147+678+902+333+92+145=13136\)

Next, divide the sum by the total number of terms

\(\displaystyle 13136\div13=1010.462\approx1010\)

So our answer is 1010

To find the mean of a data set, we will use the following formula:

\(\displaystyle \text{mean} = \frac{\text{sum of the numbers in the data set}}{\text{number of numbers in the data set}}\)

So, given the data set

\(\displaystyle 4, 2, 6, 2, 7, 9, 9, 2, 4\)

we will first find the sum.  To find the sum, we will add the numbers together.  So,

\(\displaystyle \text{sum of the numbers in the data set} = 4+2+6+2+7+9+9+2+4\)

\(\displaystyle \text{sum of the numbers in the data set} = 45\)

Now, we will find the number of numbers within the set.  To do this, we will simply count and see how many numbers are in the set. So,

\(\displaystyle \text{number of numbers in the data set} = 9\)

Now, we will use this and substitute into the formula.  We get

\(\displaystyle \text{mean} = \frac{45}{9}\)

\(\displaystyle \text{mean} = 5\)

Therefore, the mean of the data set is \(\displaystyle 5\).

Since averages are outlier sensitive, they will go up when higher values are added or go down when lower numbers are added.  Since the new test grade is higher than the average, the average will increase. 

Find the mean of the following data set:

\(\displaystyle 13,45,66,123,43,76,45,13,67,77,45\)

To find the mean, we need to add up all our terms and divide by the number of terms.

We have eleven terms, so do the following:

\(\displaystyle 13+45+66+123+43+76+45+13+67+77+45=613\)

\(\displaystyle \frac{613}{11}=55.\bar{72}\approx56\)

Find the mean of the following data set:

\(\displaystyle 10,45,65,23,76,87,23,45,12,23,67\)

Begin by finding the sum of our terms.

\(\displaystyle 10+45+65+23+76+87+23+45+12+23+67=476\)

Next, because we have 11 terms, we need to divide the sum by 11

\(\displaystyle mean=\frac{476}{11}=43.\bar{27}\approx43\)

So our mean is 43

To find the mean of a data set, we will use the following formula:

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

So, given the data set

\(\displaystyle 5, 8, 12, 7, 5, 4, 6, 5, 11\)

we can find the sum of the numbers in the set.  To find the sum, we will add all the numbers together.

\(\displaystyle \text{sum of the numbers in the set} = 5+8+12+7+5+4+6+5+11\)

\(\displaystyle \text{sum of the numbers in the set} = 63\)

Now, we will find the number of numbers within the set.  To do this, we will just count and see how many numbers are in the set.

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

Now, we can substitute what we know into the formula.  We get

\(\displaystyle \text{mean} = \frac{63}{9}\)

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

Therefore, the mean of the data set is \(\displaystyle 7\).