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**Table of Content**

The calculator determines the mean, median, mode and range for the given data set along with the sum, minimum, maximum, range, and count.

With the help of a mean, median, mode, range calculator, you can efficiently analyze data sets and compute key statistical values to gain valuable insights in no time.

In statistics, a central tendency (or measure of central tendency) is said to be a central or typical value for a probability distribution. And, the most common measures of central tendency are said to be the arithmetic mean, the median, and the mode.

In simple words, the ‘mean’ is said to be the average of all the data in a set.

Mathematically, the ‘mean’ is a kind of average, which is found by dividing the sum of a set of numbers by the count of numbers in the data set.

The median is referred to as the middle values in a given data set or it is a simple measure of central tendency, separating the upper half of a data set from the lower half.

The definition of mode states, it is the value that occurs most frequently in a data set. It is used to show the information related to the random variables and populations.

Read more! And learn how to find the mean median mode range.

Go through the following steps to find the mean:

- First of all, sum all the values
- Now count the total number of values that are present in the data set
- Divide the sum of all the values by the total number of values

The formula for the mean (arithmetic) is:

**\(\ μ =\dfrac{∑X}{N}\)**

or

**\(\ Mean =\dfrac{sum\ of\ the\ terms}{number\ of\ terms}\)**

Where;

- μ represents the population mean (well, you can use the letter M to represent the mean of a sample instead, but remember that the calculation is the same)
- ∑X indicates the sum of all the numbers
- N is referred to as the total number of values

**Example:** Find the mean for a data set, X = 2, 3, 4, 5, 6.

**Solution:**

Sum = **∑X **= 2 + 3 + 4+ 5+ 6 = 20

Total Numer of Values = N = 5

\(\ μ =\dfrac{∑X}{N}\)

\(\ μ =\dfrac{20}{5}\)

μ = 4

Here are the steps:

- Arrange data values in ascending order
- After listing the values, find the middle value of the set
- If two data values are in the middle, then the median is the mean of those 2 values

To calculate the median, the following formula will be taken into account:

Median = Middle Value of the Given Data Set

Keep in mind it’s good to use the median when there are huge variations in the values of the data set.

- First of all, you have to sort your data set numbers from least to greatest
- Now, you have to find the central number of the data set

Let’s take a look at this data set to understand the concept, 1, 2, 3, 5, 7 – you can see that there are two numbers in front of the 3, and also the two numbers behind it. It shows that 3 is the number that is exactly in the middle of the data sample.

- First of all, you ought to sort out your set of numbers in ascending order
- If there are two even numbers in the middle then, you have to find the average of the two middle numbers

In the data set 1, 1, **4**, **6**, 6, 9 the median is 5. By taking the mean of even numbers 4 and 6 we have \((\dfrac{4+6}{2})=\ 5\).

So, it’s clear that the median in an even set of numbers doesn’t have to be a number in the data set itself.

Follow the below-mentioned steps:

- To find the mode or modal value, you ought to put the numbers in ascending order
- Next, count how many of each number
- A number that appears most often is said to be the mode

Mode = Most Repeated element in a Set

**Example: **Let’s suppose you have a data sample as 3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

Now, find the Mode:

**Solution:**

Arrange these numbers:

3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56

By ordering, this becomes easy to see which numbers appear most often.

In this example, the mode of numbers is 23.

**So, what about More Than One Mode:**

Sometimes we can have more than one mode.

**Example:** {1, 3, 3, 3, 4, 4, 6, 6, 6, 9}

**Solution:**

Here you can see that 3 appears three times, as does 6.

So, it means there are two modes i:e 3 and 6

Remember that:

- If your data sample has two modes, then it is said to be “bimodal”
- If your data set has more than two modes, then it is said to be “multimodal”

Mathematically, the range of a data sets is said to be the difference between the highest/largest and smallest/lowest values in the data set. The range is a measure of variability.

Use the following formula to find range of a given data set:

Range = Highest Value – Lowest Value

**\(\ Upper\ Fence =\ Q_{3}+ 1.5\times\ Interquartile\ Range\)**

**\(\ Lower\ Fence =\ Q_{1}- 1.5\times\ Interquartile\ Range\)**