Mean, Median, Mode, Range Calculator

Mean, Median, Mode, and Range Calculator Use

The Mean Median Mode and Range Calculator makes it incredibly simple to find the mean, median, mode, and range simultaneously. You can either enter your raw data or copy and paste it into the white box. Please remember to use commas to separate numbers or values in your data set. Next, select the calculate button.

The results are ready. The Mean Median Mode and Range Calculator calculates not only the Mean, Median, Mode, and Range but also the Geometric Mean, Largest and Smallest number, Sum, Count, and returns the Sorted Data Set.

Finding a typical value to represent your data set is easier with the help of the Mean, Median, and Mode Calculator. The Range calculator can help you calculate the spread of your data set. We'll closely examine the Mean Median Mode and Range Calculator outputs.

The Mean Definition

The mean is the average of your data set's values. In other words, the mean is the sum of the data set's values divided by the total number of data values. The mean of a population is represented by μ (Mu), and the mean of a sample is represented by x̄ (X bar).

To calculate the mean of a population, you can use the below formula.

$$\mu=\frac{Sum\ of\ the\ data\ set’s\ values}{Total\ number\ of\ data\ values\ in\ the\ population}=\frac{ΣX}{N}$$

To calculate the mean of a sample, you can use the below formula.

$$\bar{X}=\frac{Sum\ of\ the\ data\ set’s\ values}{Total\ number\ of\ data\ values\ in\ the\ sample}=\frac{ΣX}{n}$$

Let's learn the mean using the example below.

Example:

Your college basketball players' heights (in meters) are given below. What is the mean height of your college basketball players?

1.75 m, 1.96 m, 1.95 m, 2.00 m, 2.05 m, 2.05 m, 2.10 m

Solution:

$$The\ mean\ height=\frac{\sum{}{}X}{N}=\frac{1.75\ m+1.96\ m+1.95\ m+2.00\ m+2.05\ m+2.05\ m+2.10\ m}{7}=\frac{13.86\ m}{7}=1.98\ m$$

The mean is calculated using all of the values in the data set. Therefore, the mean is a representative value of your data set.

You can use the mean calculator to determine more than just the arithmetic mean mentioned above. You can also use it to obtain your data set's geometric mean. The n-th root of the product of n items in your data set is known as the geometric mean.

$$Geometric\ mean=\sqrt[n]{x₁ × x₂ × x₃ × \cdots × xₙ}$$

We will find the geometric mean of the previous example.

$$Geometric\ mean=\sqrt[7]{1.75×1.96×1.95×2.00×2.05×2.05×2.10}=\sqrt[7]{118.0554}=1.977$$

The Geometric Mean is either less than or equal to the Arithmetic Mean for any set of non-negative numbers.

In our example,

$$Geometric\ mean < Arithmetic\ mean$$

$$1.977<1.98$$

The Median Definition

The median is the central point of a dataset arranged in ascending or descending order. The median calculator divides your data set into two equal parts.

$$Median=Value\ of\ \left(\frac{N+1}{2}\right)-th\ item$$

If the number of data values in your data set is odd, then the median will be the middle value of the sorted data set. The Mean Median Mode and Range calculator helps you to sort your data. If the number of data values in your data set is an even number, then the median will be the average value of the two middle points of the sorted data set.

Let's find the median for the previous example.

First, we'll arrange the data set into some order.

1.75 m, 1.95 m, 1.96 m, 2.00 m, 2.05 m, 2.05 m, 2.10 m

Now, we will find the middle point.

$$Median=Value\ of\ \left(\frac{N+1}{2}\right)-th\ item=Value\ of\ \left(\frac{7+1}{2}\right)-th\ item=Value\ of\ 4-th\ item$$

The value of the 4th item in the sorted data set is 2.00 m. Therefore,

Median = 2.00 m

Let's imagine that the basketball team adds a new player who is 1.90 m tall. Now, what is the median height of the basketball players on the team?

Now the heights of the players are as follows.

1.75 m, 1.96 m, 1.95 m, 2.00 m, 2.05 m, 2.05 m, 2.10 m, 1.90 m

First, we will arrange the data set into some order.

1.75 m, 1.90 m, 1.95 m, 1.96 m, 2.00 m, 2.05 m, 2.05 m, 2.10 m

Now, we will find the middle point.

$$Median=Value\ of\ \left(\frac{N+1}{2}\right)-th\ item=Value\ of\ \left(\frac{8+1}{2}\right)-th\ item=Value\ of\ {4.5}-th\ item$$

Since you have an even number of players, you must find the average of the two middle points. In this example, the median is the average of the 4th and 5th items.

Therefore,

$$Median=\frac{1.96\ m+2.00\ m}{2}=1.98\ m$$

The median is useful as a central tendency measure if your data set has some extreme values. The data set's extreme values do not impact the median because the median only considers middle values.

The median is a robust measure of central tendency, particularly when your data set contains outliers. Extreme values in the data set have no impact on the median because it is solely determined by the middle values. Although the median provides a good central reference point, it does not take every value in the data set into account in the way the mean does.

The Mode Definition

The mode is the most common value in a data set. In other words, a data set's mode is the most frequently occurring data value.

Let's find the mode for the previous example.

All heights of all players appear only once, except for the height of 2.05 m. Two players on the basketball team have a height of 2.05 m. Therefore, 2.05 m is the most common value in our example.

Mode = 2.05 m

In our example, since there is one mode for the data set, the data set is called unimodal. There could be even more than one mode for a data set. If there are 2 modes, we call that bimodal. If there are more than 2 modes, it is called multimodal. It is essential to know that some data sets do not have a mode if all values occur only once in the data set.

We can easily find the mode in the data set without a calculation. The mode, however, is not an accurate representation of all the values in the dataset like the mean.

The Range Definition

The range is the difference between your data set's largest and smallest value. It is the easiest measure that you can calculate to find the spread of your data set.

Range = Largest value - Smallest value

Let's learn the range using the previous example.

First, you must identify your data set's largest and smallest value to find the range. If the data set is not in order, we can use the Range Calculator to find the largest and smallest value quickly.

Then you take the difference between your data set's largest and smallest value.

Largest value = 2.10 m

Smallest value = 1.75 m

Therefore,

Range = 2.10 m - 1.75 m = 0.35 m

The range is susceptible to bias and distortion because it only considers the extreme values and ignores all other data values.