Descriptive Statistics

Central tendency (mean, median, mode) and dispersion (range, variance, SD) summarize a data set.

When to Use Each Measure

MeasureBest For
MeanSymmetric data without outliers
MedianSkewed data, income, home prices
ModeCategorical data, most common value
Std DevUnderstanding 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.