What is the difference between Mean and Median?

The mean is the calculated arithmetic average. The median is the middle point of a sorted dataset. The median is far less sensitive to extreme outliers than the mean.

Can a dataset have multiple modes?

Yes! If two or more values share the highest frequency, the dataset is bimodal or multimodal. If all values occur equally, the dataset is considered to have no mode.

What does standard deviation measure?

It measures the dispersion or spread of a dataset relative to its mean. A low standard deviation means values cluster close to the mean; a high standard deviation indicates a wider spread.

Math Tool

Average Calculator

Calculate average statistics for any dataset. Compute the arithmetic mean, median, mode, range, geometric mean, and standard deviation with detailed step explanations.

Interactive Average Calculator Workspace

Live Solver

Enter Numbers (separated by commas or spaces)

Arithmetic Mean (Avg)18

Median Value15.5

Mode(s)No Mode

Range (Max - Min)38

Comprehensive Statistical Breakdown

Sum of Elements: 108

Count of Elements (N): 6

Sorted Dataset: 4, 8, 15, 16, 23, 42

Geometric Mean: 13.9655

Population Std. Deviation (σ): 12.3153

Sample Std. Deviation (s): 13.4907

Mathematical Formula & Variables

Equation ModelMean = Σx / N | Median = Middle Value | Mode = Most Frequent

The arithmetic mean is the sum of all data points divided by the count of elements. The median is the physical middle when sorted. The mode is the value appearing most frequently.

Variable Definitions

Symbol	Description
Σx	The sum of all numbers in the dataset
N	The total number of data values in the set

How to Use the Average Calculator

Enter your dataset numbers separated by commas, spaces, or newlines.
Click Calculate to process the statistical values.
Observe the calculated results showing the Mean, Median, Mode, Range, Sum, Count, and Population Standard Deviation with complete worked calculations.

Practical Example Calculation

Scenario Context: Finding the average statistics for the dataset: 4, 8, 15, 15, 23, 42.

Step 1: Count the values (N): 6 elements.

Step 2: Calculate Sum: 4 + 8 + 15 + 15 + 23 + 42 = 107.

Step 3: Calculate Mean: Sum ÷ N = 107 ÷ 6 = 17.83.

Step 4: Calculate Median: Sort values (4, 8, 15, 15, 23, 42). The middle two are 15 and 15. Average of middle two is (15+15)/2 = 15.

Step 5: Calculate Mode: 15 is the most frequent value, appearing twice.

Step 6: Calculate Range: Maximum (42) - Minimum (4) = 38.

The dataset has a Mean of 17.83, a Median of 15, a Mode of 15, and a Range of 38.

Frequently Asked Questions

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