Descriptive Statistics
Central tendency (mean, median, mode) and dispersion (range, variance, SD) summarize a data set.
When to Use Each Measure
| Measure | Best For |
|---|---|
| Mean | Symmetric data without outliers |
| Median | Skewed data, income, home prices |
| Mode | Categorical data, most common value |
| Std Dev | Understanding spread around mean |
How to Use This Statistics Calculator
Enter a dataset (comma-separated numbers). The calculator provides a complete statistical summary: mean, median, mode, range, variance, standard deviation, quartiles, and outlier detection.
Formula & How It Works
Mean = Σx/n. Median = middle value. Q1 = median of lower half. Q3 = median of upper half. IQR = Q3 – Q1. Outliers: values beyond Q1 – 1.5×IQR or Q3 + 1.5×IQR.
Calculation Example
Data: 23, 45, 12, 67, 34, 78, 12, 56, 89, 34. Mean = 45, Median = 39.5, Mode = 12 and 34, Range = 77, SD = 25.5.
Expert Tips
Start by checking for outliers before running analysis — they can distort the mean. For skewed data, the median is more representative than the mean. Always visualize data (histogram/boxplot) before computing statistics.
Frequently Asked Questions
Mean vs Median?
Mean = average. Median = middle value. Median is better for skewed data (e.g., income) because outliers don't affect it.
What is standard deviation?
SD measures spread around the mean. ~68% of data falls within 1 SD, ~95% within 2 SDs (normal distribution).
Population vs Sample SD?
Population (σ) divides by N. Sample (s) divides by N-1. Use sample SD when data is a subset of a larger population.