Measures of Dispersion Calculator

Quickly determine how spread out your dataset is. Paste your data below to instantly calculate the standard deviation, variance, interquartile range (IQR), and range.

How to use this calculator

1. Choose Sample or Population: If your data represents a portion of a larger group, leave it on Sample (this is the most common). If you have data for every single member of the group you are studying, select Population.
2. Enter your data: Paste your numbers into the box. You can separate them with commas, spaces, or line breaks. The calculator will automatically filter out any text or extra spaces.
3. Get instant results: Click calculate to generate your descriptive statistics.

Understanding Your Results

When analysing data, knowing the center (the mean or median) is only half the story. Measures of dispersion tell you how clustered or scattered your data points are around that center.

• Standard Deviation: The most common measure of spread. It roughly represents the average distance of each data point from the mean. A low standard deviation means the data is tightly clustered; a high standard deviation means it is widely spread out.
• Variance: The average of the squared differences from the mean. While it is mathematically crucial (it is exactly the standard deviation squared), it is harder to interpret on its own because the units are squared.
• Interquartile Range (IQR): The difference between the 75th percentile (Q3) and the 25th percentile (Q1). The IQR represents the “middle 50%” of your data. Unlike the standard deviation, the IQR is not skewed by extreme outliers.
• Range: The simplest measure of spread, calculated by subtracting the lowest value in your dataset from the highest value.

Why is there a Sample vs. Population toggle?

When calculating variance and standard deviation for a sample, statisticians divide by the number of data points minus one ($n-1$) rather than the total number of data points ($n$). This is a mathematical adjustment (known as Bessel’s correction) that prevents the formula from underestimating the true spread of the larger population. Our calculator handles this adjustment for you automatically based on the toggle you select.