Calculate Mean, Median, Mode, and Range!

Use this statistics calculator to find the Mean, Median, Mode and Range measurements for a set of values.

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How to use the Mean, Median, Mode and Range Calculator?

Calculator features

🔢 Data set length:	Unlimited
⚡ Speed of Computation:	Instant!
➡️ Calculator Output:	Display, Copy, Save
🎯 Calculator Accuracy:	100%
📋 Definitions and Formulas:	Available

Mean, or Average

What is the Mean? Mean definition in statistics

The mean is the arithmetic average of a given set of numbers. It is a measure of central tendency.

The mean is tipically denoted as x̄, pronounced “x bar.

How to Calculate the Mean

The mean is simply the sum of all the values, divided by the total number of values.

Follow these steps to calculate the mean of a set of values:

1. Add up all data values to get the sum.
2. Count the number of values in your data set.
3. Divide the sum by the count

Example

Let’s find the mean of 3, 7, 11, 17:

3 + 7 + 11 + 17 = 38

Now let’s divide 38 by the number of values, which in our case is 4.

38 / 4 = 9.5

You can use the mean calculator at the top of this page to easily find the mean of a set of values.

Mean Formula

$$\text{mean}=\overline{x}={\displaystyle \frac{\sum _{i=1}^n{x}_i}{n}}$$

Median, or Middle Value

What is the Median? Median definition in statistics

The median is the middle of a sorted set of number. It divides a data set into two halves.

The median is a measure of central tendency, and it represents the point in relation to which half of the values are lower and half are higher. In other words, it is the central point of an ordered set of values.

How to Calculate the Median?

1. Sort the data set arranging its values from lowest to highest.
2. If the data set has an odd number of values, find the value in the middle of the set (the median data point separating the upper half of the data values from the lower half)
3. If the data set has an even number of values, find the two values in the middle of the set (the median data points separating the upper half of the data set from the lower half) and then calculate their mean, which will be the median.

Example

Let’s find the median of an odd data set: 1, 2, 3, 8, 9:

The median value is 3.

Now let’s find the median of an even data set: 1, 2, 3, 8, 9, 10:

Take the mean of the two values in the middle: ( 3 + 8 ) / 2 = 5.5.

You can use the median calculator at the top of this page to easily find the median of a set of values.

Median Formula (for data sets of Odd size)

If the size of the data set n is odd the median is the value at position p where

$$p={\displaystyle \frac{n+1}{2}}$$ $$\tilde{x}=x_p$$

Median Formula (for data sets of Even size)

If n is even the median is the average of the values at positions p and p + 1 where

$$p={\displaystyle \frac{n}{2}}$$ $$\tilde{x}={\displaystyle \frac{x_p+x_{p+1}}{2}}$$

Mode, or Most Frequent Value

What is the Mode? Mode definition in statistics

The mode is the value that appears the most often in a given data set.

The mode represents the value that is most likely to be observed, i.e. the typical values.

A data set may have:

• No mode (when there are no repeating values, or when all values occur the same number of times), or
• One mode (when one single value occurs most of the times), or
• More than one mode (when two or more single values occur most of the times).

How to Calculate the Mode

1. Count how many times each individual value appears in the data set.
2. The value(s) that occur most frequently is (are) the mode(s).

Examples

The mode for the data set 1, 2, 3, 3, 4, 5 is 3.

The modes for the data set 1, 2, 3, 3, 4, 4, 5 are 3 and 4.

Both the data sets 1, 1, 1 and 1, 2, 3, 4, 5 have no mode.

You can use the mode calculator at the top of this page to easily find the mode(s) of a set of values.

Mode Formula

${\displaystyle \frac{(f_m-f_1)}{(f_m-f_1)+(f_m-f_2)}}$

Where:

• L is the lower limit of the modal class.
• h is the size of the class interval.
• f_m is the frequency of the modal class.
• f₁ is the frequency of the class preceding the modal class.
• f₂ is the frequency of the class succeeding the modal class

Range

What is the Range? Range definition in statistics

The range is simply the difference between the largest and the smallest number within a given set of data.

The range of a data set is a measure of dispersion of the data set itself, and it represents by how much the values in the data set are likely to differ from their mean.

How to Calculate the Range

1. Find the highest value in the data set.
2. Find the lowest value in the data set.
3. Subtract the lowest value from the highest value.

Example

Let’s find the range for 1, 2, 3, 4, 5:

The highest value is 5, and the lowest is 1.

In this case the range is 5 – 1 = 4.

You can use the range calculator at the top of this page to easily find the range of a set of values.

Range Formula

Range = maximum(x_i) – minimum(x_i)