**Statistics Calculators** ▶ Midrange Calculator

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**Table of Content**

Our free midrange calculator is the simplest and the most convenient way to find the midrange of a data set. Once click away and find the maximum and the minimum values of the input numbers. With this maximum and minimum calculator, you can also find other basic statistics including median, mode, standard deviation, variance, range, summation, and count number.

Let’s move on!

Midrange statistics are the arithmetic mean of the maximum and minimum values in a data set.

**Formula:**

The following is the midrange formula:

M = X_max + X_min / 2

Where,

- M is midrange
- X_max is the maximum value in a data set
- X_min is the minimum value in a data set

**Example:**

How to find the midrange of a data set {6,6,12,15,7}

Solution:

The minimum value of a data set (Min. Value): 6

The maximum value of a data set (Max. Value): 15

Midrange = (Min. Value + Max. Value) / 2 = (6 + 15) / 2 = 10.5

Right now, we discuss some other basic statistics that are related to midrange math and you can find these basic parameters with this midrange calculator.

The middle number in a sorted, ascending or descending list of numbers is known as the median of the number ( or taking the mean if there are two middle numbers).

**Example**

Find the median of the data set {3, 13, 2, 34, 11, 26, 47}

**Solution:**

The sorted order becomes {2, 3, 11, 13, 26, 34, 47}

Therefore, the median is the number in the middle {2, 3, 11, 13, 26, 34, 47} is 13.

The most frequent number that occurs many times in a data set is the mode.

You can also determine this particulate mode by subjecting this free online minimum and maximum calculator.

**Example**

The mode of {4, 2, 4, 3, 2, 2} is 2 because it occurs three times.

The difference between the highest value and the lowest value is called range.

Formula

Range = Maximum value – Minimum value

**Example**

Find the range of a data set {53, 50, 60, 51, 48, 93, 80, 92, 71, 90}

Solution:

Arrange the following numbers in ascending order, we get;

48, 50, 51, 53, 60, 71, 80, 90, 92, 93

Range = Maximum value – Minimum value

Range = 93 – 48 = 45

Thus, 45 is the required range.

The average amount of variability in your dataset is known as the standard deviation (or σ).

Formula

$$ σ = \sqrt{\frac{1}{N} \sum_{i=1}^N\left(x_{i} – μ\right)^2} $$

Where,

- σ = sample standard deviation
- ∑ = sum of…
- X = each value
- x̅ = sample mean
- n = number of values in the sample

Variance is defined as a measure of how data points differ from the mean

Formula

$$ σ2 = ∑(xi – μ)^2 / N $$

where

- σ2 is a variance;
- μ is the root mean square
- xᵢ represents the i-th data point among the N shared data points.

When it comes to finding standard deviation and variance values, the midrange calculator will help you in this regard.

Right now, look at the following example that is specifically solved to clarify the answer and verify the concept with respect to this midrange calculator.

**Example**

How to calculate midrange for the data set values of 2, 6, 7, 11, 32.

**Solution:**

Given data set values are 2, 6, 7, 11, 32

Formula to calculate midrange

M = maximum + minimum / 2

Max = 32

Min = 2

M = 32+2 / 2

M = 34/2

M = 17

Hence, the mid-range of the data set values ie., 2, 6, 7, 11, 32 is 17.

Let’s see this free midrange calculator that determines how to find midrange in statistics. Let’s move on and have a look at the work of this calculator!

**Input**

Just enter the data set (numbers separated by commas) into the designated box.

After that, make a tap on the ‘calculate’ button

**Output**

The free find means median mode midrange calculator does the following results:

Determines the mid range calculation

Also determines other basic statistics including median, mode, standard deviation, variance, range, summation, and count number.

Yes, both mode or modal values are the same and the most common number in a data set. Generally, It is useful in the statistics field because it can tell you what the most popular item in your data set is.

The average is calculated by adding all of the individual values in the data set and dividing this total by the number of observations. Whereas, the median is calculated by taking the “middle” value, the value for which half of the observations are larger and half are smaller.

Therefore, you can find the median with our mid range calculator.

A small variance has indicated that the data points tend to be very close to the mean, and to each other. On the other hand, A high variance has indicated that the data points are very spread out from the mean, and from one another.

Midrange formula plays an important role in the fields of statistics, physics, maths, and engineering. The midrange statistics are of great help when you need to find the midpoint of a large data set and it also provides an alternative calculation of basic statistics for the measure of central tendency. Feel free to make use of this online midrange calculator for various solutions within fractions of seconds.

From the source of Wikipedia: Mid-range, Range (statistics), median

From the source of khan academy: Step-by-step interactive example for calculating standard deviation