# Median Calculator

Median Calculator is used to compute and display the median of a list of given values or a set of data. In statistics as well as probability theory, the median can be defined as a value that separates the two halves (upper and lower) of an organized probability distribution or a data sample.

## What is Median Calculator?

Median Calculator is an online tool that can effectively determine the median of a given data set. Mean, median, and mode are the three measures of central tendency. Median is used to analyze and draw logical conclusions from statistical data efficiently. To use the * median calculator* enter the values within the brackets separated by commas.

## How to Use Median Calculator?

Follow the steps given below to find the median of a given set of data using the median calculator:

**Step 1:**Go to Cuemath's online median calculator.**Step 2:**Enter the values in the input box of the median calculator.**Step 3:**Click on**"Calculate"**to find the median of those values.**Step 4:**Click on**"Reset"**to clear the field and enter a new set of values.

## How Does Median Calculator Work?

The value of the middlemost observation obtained after arranging the data in ascending order is called the median of the data. When we have to find the mid-value of a data set that is highly skewed and asymmetrical we use the median. Suppose we need to establish the typical income of a bunch of people. The data set (here the income of the people) will have a lot of variations. Thus, if we choose the median to find the typical income value it will yield more accurate results as compared to the mean. To find the median of a given set of values, follow the steps given below:

**Step 1:**Arrange the values in ascending order.**Step 2:**Count the number of values. This is given by n.**Step 3:**Plug this value into the formula given below to find the median.

If **n is odd**, then use the formula:

\(\left(\frac{n+1}{2}\right)^{t h} \mathrm{obs}\)

If **n is even**, then use the formula:

\(\frac{\frac{n}{2} \text { obs. }+\left(\frac{n}{2}+1\right)^{t h} \text { obs. }}{2}\)

## Solved Examples on Median

**Example 1:** Find the median for the dataset: {1,2,2,3,4,3,3} and verify it using the median calculator.

**Solution:**

- Arrange the values in ascending order: {1,2,2,3,3,3,4}.
- Count the number of values/observations: n = 7.
- The number of observations is odd.
- Putting n = 7 in the formula (n + 1)/2 gives us (7 + 1) / 2 = 4
- Thus the 4th observation is the median. From the data set this value is 3.

Therefore, the median of the given dataset = {3}

**Example 2:** Find the median for the dataset: {56, 89, 32,12, 90, 111, 20, 99} and verify it using the median calculator.

**Solution:**

- Arrange the values in ascending order: {12, 20, 32, 56, 89, 90, 99, 111}.
- Count the number of values/observations: n = 8.
- The number of observations is even.
- Putting n = 8 in the formula.

\(\frac{\frac{n}{2} \text { obs. }+\left(\frac{n}{2}+1\right)^{t h} \text { obs. }}{2}\)

= \(\frac{\frac{8}{2} \text { obs. }+\left(\frac{8}{2}+1\right)^{t h} \text { obs. }}{2}\)

= (4^{th} obs. + 5^{th} obs.)/2

= (56 + 89) / 2

= 72.5

Therefore, the median of the given dataset = 72.5

Now, you can use this median calculator and find the median for the following set of values:

- {120,133,157,109,112,294,140,134}
- {200,235,225,330,219}
- {56,55,56,70,82,56,70,67,76,69,81,72}

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