Descriptive Statistics Calculator

Descriptive statistics summarize a dataset with a small set of numbers that capture its center, spread, and shape. They are the first thing any data analyst computes, before modeling, before inference, before anything else.

Measures of center:

• Mean: sum of values divided by count. Sensitive to outliers.
• Median: middle value when sorted. Robust to outliers. A billionaire moving into your neighborhood changes the mean income dramatically but barely moves the median.
• Mode: most frequently occurring value (can have multiple or none).

Measures of spread:

• Range: max minus min. Sensitive to extreme values.
• Variance: average squared distance from the mean. Squaring penalizes large deviations heavily. Sample variance divides by n-1 (Bessel’s correction) to reduce bias when estimating a population.
• Standard deviation: square root of variance, in the original units. About 68% of normally distributed data falls within 1 SD of the mean; 95% within 2 SD.
• IQR (Interquartile Range): Q3 minus Q1. The middle 50% of the data. Robust to outliers and more useful than range for skewed distributions.

Q1 is the median of the lower half, Q3 the median of the upper half. A data point counts as an outlier if it falls more than 1.5×IQR below Q1 or above Q3, which is where the whiskers of a box plot stop. The calculator applies that rule and names any value that breaks it.

Mean against median is the quickest read on skew. If they sit close together the distribution is roughly symmetric. If the mean is well above the median, something is dragging the right tail out; below, and the tail runs left. Income data is the standard case, and it is why every report on household earnings quotes the median.

The chart sorts your values smallest to largest and draws them as bars, with the mean marked as a horizontal line across them. Sorting is what makes it readable: a long flat stretch is where the data clusters, a sudden step is a gap, and a lone tall bar at either end is the outlier you should go and check before trusting the mean.