Deviation From the Mean Calculator

Calculator Input

Formula Used

Mean: x̄ = Σx / n

Deviation from mean: d = x - x̄

Absolute deviation: |d| = |x - x̄|

Squared deviation: d² = (x - x̄)²

Mean absolute deviation: MAD = Σ|x - x̄| / n

Population variance: σ² = Σ(x - x̄)² / n

Sample variance: s² = Σ(x - x̄)² / (n - 1)

A positive deviation means the value is above the mean. A negative deviation means the value is below the mean. A zero deviation means the value equals the mean.

How to Use This Calculator

1. Enter your dataset values in the values box.
2. Separate values with commas, spaces, semicolons, or new lines.
3. Choose calculated mean or enter a custom mean.
4. Select decimal places for the result table.
5. Press the calculate button.
6. Review deviations, variance, and standard deviation.
7. Use CSV or PDF buttons to export the report.

Example Data Table

Deviation From the Mean Guide

What This Calculator Shows

Deviation from the mean shows how far each value sits from the center of a dataset. It is one of the simplest ways to study spread. A value near the mean has a small deviation. A value far from the mean has a large deviation. This calculator lists every value, its deviation, absolute deviation, and squared deviation. It also gives useful summary measures.

Why Deviation Matters

The mean alone can hide important differences. Two datasets may have the same mean. Yet one dataset may be stable. The other may be widely spread. Deviation helps reveal that difference. Teachers can compare scores. Analysts can study sales changes. Engineers can review quality data. Researchers can inspect measurement variation.

Advanced Output

This tool goes beyond a single answer. It calculates total deviation, mean absolute deviation, population variance, sample variance, and both standard deviations. The absolute deviation ignores direction. It focuses only on distance from the mean. Squared deviation gives more weight to large differences. That makes it useful for variance and standard deviation.

Calculated Mean and Custom Mean

You can let the calculator find the mean automatically. You can also enter a custom mean. A custom mean is useful when comparing values against a target, benchmark, expected average, or historical standard. For example, a factory may compare daily output against a required target. A teacher may compare scores against a passing average.

Reading the Results

Positive deviations show values above the mean. Negative deviations show values below the mean. A zero value means no difference from the mean. The largest absolute deviation marks the value farthest from the center. Use the export buttons when you need a record. The CSV file works well for spreadsheets. The PDF file is useful for reports.

FAQs

What is deviation from the mean?

Deviation from the mean is the difference between one value and the dataset mean. It shows whether the value is above, below, or equal to the average.

How do I calculate deviation from the mean?

First calculate the mean. Then subtract the mean from each value. The formula is value minus mean.

Can deviation be negative?

Yes. A negative deviation means the value is below the mean. A positive deviation means it is above the mean.

What is absolute deviation?

Absolute deviation is the distance from the mean without a plus or minus sign. It uses the absolute value of each deviation.

What is mean absolute deviation?

Mean absolute deviation is the average of all absolute deviations. It shows the typical distance from the mean.

Why is squared deviation used?

Squared deviation removes negative signs and gives larger differences more weight. It is used for variance and standard deviation.

Should I use sample or population variance?

Use population variance when your data includes every value in the group. Use sample variance when your data represents a larger group.

Can I export the results?

Yes. After calculation, you can download the detailed deviation table as a CSV file or a PDF report.