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Statistics Calculator
Paste your dataset below to get a complete summary profile of descriptive statistics, central tendency, quartiles, outliers, and variance.
Calculate descriptive statistics
Descriptive Statistics
| Count (N) | — |
|---|---|
| Minimum (Min) | — |
| Maximum (Max) | — |
| Range | — |
| Sum | — |
| Mean (Arithmetic) | — |
| Median | — |
| Mode | — |
| Geometric Mean | — |
| First Quartile (Q1) | — |
| Third Quartile (Q3) | — |
| Interquartile Range (IQR) | — |
| Outliers | — |
| Sample Std. Deviation (s) | — |
| Sample Variance (s²) | — |
| Population Std. Deviation (σ) | — |
| Population Variance (σ²) | — |
| Std. Error of Mean (SEM) | — |
What is Descriptive Statistics?
Descriptive statistics summarize and describe the features of a dataset. They provide a quick overview of the central tendency, dispersion, and overall distribution of the data.
Central Tendency
Central tendency indicates where the center of the dataset lies. It is measured by the:
- Mean: The arithmetic average (Sum divided by Count).
- Median: The middle value when sorted.
- Mode: The most frequently occurring value(s).
- Geometric Mean: The n-th root of the product of all values (useful for growth rates).
Dispersion and Variability
Dispersion describes the spread of the data points:
- Range: The difference between the maximum and minimum values.
- Standard Deviation: The typical distance of data points from the mean.
- Variance: The average of squared differences from the mean.
- Quartiles (Q1 & Q3): The values that divide the sorted data into four equal parts.
- IQR (Interquartile Range): The range of the middle 50% of the data (Q3 - Q1).
- Standard Error (SEM): Standard deviation divided by the square root of the sample size. It measures how much the sample mean is expected to vary from the true population mean.
Identifying Outliers
Outliers are data points that lie abnormally far from the rest of the values. A common way to identify outliers is the **IQR Method**:
Any value that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.
FAQ
When should I use sample vs. population standard deviation?
Use the sample standard deviation if your dataset represents a smaller subset of a larger population. Use the population standard deviation if you have collected data for every single member of the target population.
Why can't the geometric mean be calculated with negative numbers?
The geometric mean involves multiplying all numbers together and taking the n-th root. If there are negative numbers or zero, taking roots of negative numbers can yield complex numbers, and multiplying by zero results in a product of zero. Therefore, it is only defined for strictly positive numbers.