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Mean Median Mode Range Calculator

Enter the required data values into the calculator, separated by commas, spaces, or line breaks, and instantly compute the mean, median, mode, and range.

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The mean, median, mode, and range calculator allows you to quickly determine key statistics for any dataset. It also provides the sum, minimum, maximum, count, and overall variability of the numbers. Using this calculator, you can efficiently analyze datasets and gain insights in seconds.

What Are Mean, Median, and Mode?

In statistics, central tendency measures summarize a dataset by identifying a central or typical value. The three most common measures of central tendency are the mean, median, and mode.

The mean is the average of all values in a dataset, calculated by dividing the sum of the numbers by the total count. The median is the middle value when the data is ordered from smallest to largest. The mode is the value that occurs most frequently in the dataset, often used to describe the distribution of values.

How To Calculate Mean?

Steps to calculate the mean:

Add together all the values in the dataset.
Count the total number of values.
Divide the sum by the total number of values to find the mean.

Mean Formula:

\(\mu = \dfrac{\sum X}{N}\)

\(\text{Mean} = \dfrac{\text{sum of values}}{\text{number of values}}\)

Where:

\(\mu\) = population mean (or M for sample mean)
\(\sum X\) = sum of all data points
N = total number of data points

Example:

Find the mean for the dataset: 2, 3, 4, 5, 6.

Solution:

Sum = 2 + 3 + 4 + 5 + 6 = 20

Total number of values = 5

Mean = 20 ÷ 5 = 4

How To Find The Median?

Steps to determine the median:

Arrange the data in ascending order.
Identify the middle value.
If there are two middle values, calculate their average.

Median Formula:

\(\mathrm{Med}(X) = \begin{cases} X\left[\frac{n+1}{2}\right], & \text{if n is odd} \\ \frac{X\left[\frac{n}{2}\right] + X\left[\frac{n}{2}+1\right]}{2}, & \text{if n is even} \end{cases}\)

Odd Number of Values:

Example: Dataset 1, 2, 3, 5, 7 → Middle value is 3. Median = 3.

Even Number of Values:

Example: Dataset 1, 1, 4, 6, 6, 9 → Middle values are 4 and 6. Median = (4+6)/2 = 5.

How To Find The Mode?

Steps to determine the mode:

Arrange the dataset in ascending order.
Count how many times each value appears.
The value(s) with the highest frequency is the mode.

Mode Formula:

Mode = Most frequent value in the dataset

Example:

Dataset: 3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29 → Mode = 23

Multiple Modes:

Dataset: 1, 3, 3, 3, 4, 4, 6, 6, 6, 9 → Modes = 3 and 6 (bimodal)

Bimodal = dataset with 2 modes
Multimodal = dataset with more than 2 modes

What Is The Range?

The range measures the spread of a dataset by calculating the difference between the largest and smallest values.

Range Formula:

Range = Highest Value - Lowest Value

Outliers:

Outliers can be detected using the 1.5 × IQR rule:

\(\text{Upper Fence} = Q_3 + 1.5 \times \text{IQR}\)

\(\text{Lower Fence} = Q_1 - 1.5 \times \text{IQR}\)

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