How to Use the Average Calculator?
To use this calculator, simply enter or paste the numbers you want to average into the box.
You can separate the numbers with spaces, commas, tabs, or put each number on a separate line. The calculator will automatically show the average as you type, along with helpful details like the number of values, median, largest value, and lowest value.
You can also drop a text file—such as a comma-separated values (CSV) or tab-separated values (TSV) file—into the box to calculate the average from the numbers in the file.
What is an average?
An average is a single number used to represent a group of numbers. It gives us a general idea of what the values in a set are like without requiring us to look at every value separately.
For example, if a student receives different marks on five tests, the average mark can be used to describe the student’s overall performance. Similarly, we might calculate the average temperature during a week, the average height of a group of students, or the average amount of money spent each day.
How to Calculate the Average
To calculate the average of a set of numbers, you first add all the numbers together and then divide the total sum by the number of values.
The formula is:
\[ \text{Average}=\frac{\text{Sum of all values}}{\text{Number of values}} \]
Example 1: Calculating the Average
Suppose five students scored 72, 85, 66, 89, and 63 on a test. The average test score is:
\[ \text{Average}=\frac{72+85+66+89+63}{5}=75 \]
Therefore, the average test score is 75.
Notice that 75 does not have to be one of the original scores. An average represents the group as a whole, so it can be a value that does not actually appear in the data.
Example 2: Calculating the average to find the equal share
Another useful way to understand an average is to think of it as an equal share. Imagine that three people have 5, 10, and 3 apples. Altogether, they have:
\[ 5+10+3=18 \]
If all 18 apples were shared equally among the three people, each person would receive:
\[ \frac{18}{3}=6 \]
So the average number of apples is 6.
Some people originally had more than 6 apples and some had fewer, but 6 is the amount each person would have if the total were distributed equally.
Example 3: Average of Negative and Positive Numbers
Averages can also be calculated when some values are negative. This is useful for quantities such as temperatures below zero, gains and losses, or changes in elevation.
Suppose the temperatures during four winter mornings are −4°C, −2°C, 3°C, and 7°C. Their average is:
\[ \text{Average}=\frac{-4+(-2)+3+7}{4}=\frac{4}{4}=1 \]
The average temperature is 1°C.
When negative numbers are involved, remember that they reduce the total. Do not simply ignore the negative signs.
Example 4: Finding a Missing Value Using the Average
Sometimes you may know the average and most of the values but need to find one missing value. In this situation, the average can be used to find the total first.
Suppose the average of five test scores is 80. Four of the scores are 72, 85, 78, and 90. What is the fifth score?
The relationship between the average, total, and number of values can also be written as:
\[ \text{Sum of all values}=\text{Average}\times\text{Number of values} \]
Since five scores have an average of 80, their total must be:
\[ \text{Total}=80\times5=400 \]
Now add the four known scores:
\[ 72+85+78+90=325 \]
The missing score must make the total equal to 400:
\[ 400-325=75 \]
Therefore, the missing score is 75.
Other Types of Average
The arithmetic mean is the most common type of average and works well in many everyday situations. However, it is not always the best way to represent a set of values. An unusually high or low value can sometimes pull the average away from what is typical, while certain types of data involving ratios, percentages, or repeated changes are better described in a different way.
For these situations, other measures such as the median and geometric mean can provide a more meaningful picture of the data.
Median
The median is another way of describing the center of a group of numbers. Unlike the arithmetic average, it is found by arranging the numbers from lowest to highest and identifying the middle value.
For example, consider:
\[ 3,\ 5,\ 7,\ 9,\ 12 \]
The middle value is 7, so the median is 7.
If there is an even number of values, there will be two middle values. In that case, their average is used. For example, in the data set:
\[ 4,\ 6,\ 8,\ 10 \]
the middle values are 6 and 8, so the median is:
\[ \frac{6+8}{2}=7 \]
The median can be especially useful when a set contains an unusually high or low value because it is less affected by extreme values than the arithmetic mean.
Geometric Mean
The geometric mean is another type of average, but it is calculated differently from the arithmetic mean. Instead of adding the values, the values are multiplied together and a root is taken.
For two positive numbers \(a\) and \(b\), the geometric mean is:
\[ \text{Geometric Mean}=\sqrt{ab} \]
For example, the geometric mean of 4 and 9 is:
\[ \sqrt{4\times9}=\sqrt{36}=6 \]
The geometric mean is useful in certain situations involving multiplication, ratios, or rates of change.
