Dispersion Calculator

Dispersion describes how spread out or scattered the values in a dataset are around the central value (mean or median). High dispersion means the data points vary widely; low dispersion means they are clustered closely together. Common measures include range, variance, standard deviation, and IQR.

Population standard deviation (σ) is used when your data represents an entire group and divides by N. Sample standard deviation (s) is used when your data is a subset of a larger population and divides by N−1 (Bessel's correction) to produce an unbiased estimate. If you're unsure, choose 'Sample'.

The IQR is the difference between the third quartile (Q3, the 75th percentile) and the first quartile (Q1, the 25th percentile): IQR = Q3 − Q1. It represents the spread of the middle 50% of the data and is resistant to outliers, making it useful when your dataset contains extreme values.

Dispersion tells you how reliable or consistent your data is. Two datasets can have the same mean but very different spreads — one might be tightly clustered while the other is wildly variable. Understanding dispersion helps in risk analysis, quality control, scientific research, and interpreting statistical results correctly.

The coefficient of variation (CV) expresses standard deviation as a percentage of the mean: CV = (SD / Mean) × 100. It allows you to compare the relative variability of datasets that have different units or very different means. A lower CV indicates less relative variability.

Mean Absolute Deviation (MAD) is the average of the absolute differences between each data point and the mean: MAD = Σ|xᵢ − x̄| / n. Unlike variance, it is expressed in the same units as the original data and is less sensitive to extreme outliers than standard deviation.

Standard deviation is simply the square root of the variance: SD = √Variance. So if the variance of a population is 182.2, the standard deviation is √182.2 ≈ 13.50. This calculator computes both values automatically from your entered data.

Yes. You can type or paste numbers separated by commas, spaces, or line breaks into the Data Values field. The calculator automatically filters out any empty or non-numeric entries, so you don't need to clean your data manually before entering it.