Descriptive Statistics: Understand Your Data at a Glance
What is Descriptive Statistics?
Descriptive statistics summarize a data set with a small set of indicators: central tendency (mean, median, mode), dispersion (standard deviation, variance, range, interquartile range) and shape (skewness, kurtosis). It is the foundation for inferential statistics, control charts and capability analysis, and the first step with any data is to get a quick sense of magnitude, spread and distribution before deciding which method to use. Building this data intuition before modeling is the standard order of statistical work.
When to Use It
Use descriptive statistics as a quick health check when you first receive data, for the summary tables in reports, to judge whether data are suitable for normality tests or capability analysis, and before comparing multiple groups. It is also the most common tool for explaining data characteristics to colleagues without a statistics background, and report openings routinely quote its output.
How to Use It (Step by Step)
Paste a single column of numeric data; the tool outputs the mean, median, mode, standard deviation, variance, quartiles, skewness, kurtosis and the 95% confidence interval for the mean, plus a histogram. Compare the mean with the median to detect skew or outliers, use the coefficient of variation (standard deviation divided by mean) for relative dispersion, and confirm the distribution shape with the histogram. An AI interpretation summarizes the key signals.
Key Formulas / Example
Key statistics: sample mean x-bar = sum(x) / n, sample standard deviation s = sqrt(sum((x - x-bar)^2) / (n - 1)), and the 95% confidence interval for the mean is x-bar plus or minus t * s / sqrt(n). Skewness near 0 with kurtosis near 3 matches a normal distribution; absolute skewness above 1 or kurtosis clearly away from 3 suggests non-normality that a normality test should confirm.