# Mean Median Mode Calculator

Mean Median Mode Calculator helps to calculate the mean, median, and mode of the given data set. In Statistics, there are three measures of central tendency, namely, mean, median and mode.

## What is Mean Median Mode Calculator?

Mean Median Mode Calculator is an online tool that helps to determine the measures of central tendency, that is, the mean, median, and mode for the given data set. To use this * mean median mode calculator*, enter the values within brackets separated by commas in the given input box.

### Mean Median Mode Calculator

## How to Use Mean Median Mode Calculator?

Please follow the steps below to find the mean, median, and mode for the given data set using the mean median mode calculator:

**Step 1:**Go to Cuemath's online mean median mode calculator.**Step 2:**Enter the numbers, within brackets, separated by commas in the given input box.**Step 2:**Click on the**"Calculate"**button to find the mean, median, and mode for the given numbers.**Step 3:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Mean Median Mode Calculator Work?

1. The** **mean of a given data is defined as the sum of all observations divided by the total number of observations. The mean is also known as the average. The mean is calculated using the formula:

\(\overline{x}\) = (\(x_{1}\) + \(x_{2}\) + ... + \(x_{n}\)) / n

\(\overline{x}\) = \(\sum_{1}^{n}\frac{x_{i}}{n}\)**,**

where \(x_{i}\) = \(x_{1}\),_{ }\(x_{2}\),_{ }\(x_{3}\), . . . , \(x_{n}\)

n = total number of terms

2. When we arrange the given data set in ascending order, the value of the observation that lies in the middle is known as the median. To find the median of a given set of values the formula is given as:

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

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

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

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

3. Mode for ungrouped data is found by selecting the most frequent item on the list.

## Solved Examples on Mean Median Mode

**Example 1:** Find the mean median and mode of the data set {2, 1, 2, 4, 3} and verify it using the mean median mode calculator.

**Solution:**

Arranging the data set in ascending order we get {1, 2, 2, 3, 4}.

Number of observations, n = 5

Mean

Mean = \(\sum_{1}^{n}\frac{x_{i}}{n}\)

= (1 + 2 + 2 + 3 + 4) / 5

= 12 / 5

= 2.4

Median

As the number of observations is odd,

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

= [(5 + 1) / 2]^{th} observation.

= 3^{rd} Observation.

The 3^{rd} observation is 2 thus, median = 2

Mode

As 2 is the most frequently occurring observation thus mode = 2.

**Example 2:** Find the mean median and mode of the data set {6, 3.2, 5.2, 3.5, 4} and verify it using the mean median mode calculator.

**Solution:**

Arranging the data set in ascending order we get {3.2, 3.5, 4, 5.2, 6}.

Number of observations, n = 5

Mean

Mean = \(\sum_{1}^{n}\frac{x_{i}}{n}\)

= (3.2 + 3.5 + 4 + 5.2 + 6) / 5

= 21.9 / 5

= 4.38

Median

As the number of observations is odd,

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

= [(5 + 1) / 2]^{th} observation.

= 3^{rd} Observation.

The 3^{rd} observation is 2 thus, median = 4

Mode

There is no mode as all observations occur only once.

Similarly, you can try the mean median mode calculator for the following values:

- {2, 3, 1, 1, 1, 8}
- (10.1, 6.3, 7.1, 6.3, 1.5}

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