What Are Descriptive Statistics?
Descriptive statistics summarize and describe the main features of a dataset. They provide simple summaries about the sample and measures, forming the basis for virtually every quantitative analysis. Unlike inferential statistics, they do not draw conclusions beyond the immediate data.
The three main aspects described are central tendency (mean, median, mode), dispersion (range, variance, standard deviation), and shape (skewness, kurtosis). Together these paint a complete picture of your data distribution.
Key Measures
| Measure | Type | Robust to Outliers? |
|---|---|---|
| Mean | Central Tendency | No |
| Median | Central Tendency | Yes |
| Mode | Central Tendency | Yes |
| Std Deviation | Dispersion | No |
| IQR | Dispersion | Yes |
| Range | Dispersion | No |
Formulas
Interpretation
If mean > median, the distribution is right-skewed (positively skewed). If mean < median, it is left-skewed. Equal mean and median suggest symmetry. High standard deviation relative to the mean indicates high variability.
Frequently Asked Questions
When should I use median instead of mean?
Use median when data has outliers or is skewed. Income data, home prices, and response times are typically better summarized by median because extreme values distort the mean.
Sample vs population standard deviation?
Sample SD divides by n-1 (Bessel's correction); population SD divides by n. Use sample SD (the default here) when data represents a sample from a larger population.
What is a good standard deviation?
There is no universal threshold. A "good" SD depends on context. The coefficient of variation (SD/mean) allows comparison across datasets with different scales.