Statistics Calculator

Statistics Calculator — What It Does

Enter a list of numbers (comma or newline separated) and instantly compute a full descriptive statistics summary: count, sum, mean, median, mode, range, variance (population and sample), standard deviation, quartiles (Q1, Q2, Q3), interquartile range (IQR), minimum, and maximum. Useful for data analysis, homework, quality control, and quick exploratory data analysis (EDA).

Statistics Formulas Reference

• Mean — Σx / n
• Median — Middle value of sorted data (average of two middle values for even n)
• Population Variance — Σ(x − μ)² / N
• Sample Variance — Σ(x − x̄)² / (N−1)
• Standard Deviation — √Variance
• IQR — Q3 − Q1

Example Calculation

Dataset: 4, 8, 6, 5, 3, 2, 8, 9, 2, 5

• Count = 10, Sum = 52, Mean = 5.2
• Sorted: 2, 2, 3, 4, 5, 5, 6, 8, 8, 9 → Median = 5.0
• Mode = 2, 5, 8 (all appear twice)
• Min = 2, Max = 9, Range = 7
• Sample Std Dev ≈ 2.49, Q1 = 3, Q3 = 8, IQR = 5

When to Use Each Measure

• Mean — Best for symmetric distributions without outliers (test scores, measurements)
• Median — Best for skewed data or when outliers are present (income, house prices)
• Mode — Best for categorical data or finding the most common value
• Std Dev — Measures spread around the mean; compare datasets of the same scale
• IQR — Measures spread of the middle 50%; robust to outliers unlike std dev

Frequently Asked Questions

What is the difference between mean, median, and mode?

Mean is the arithmetic average: sum all values and divide by count. Median is the middle value when sorted — it is resistant to outliers. Mode is the most frequently occurring value. For skewed distributions (like income), median is usually more representative than mean.

What is the difference between population and sample standard deviation?

Population standard deviation (σ) divides by N — use when your data is the entire population. Sample standard deviation (s) divides by N−1 (Bessel's correction) — use when your data is a sample drawn from a larger population. Sample std dev is larger and provides an unbiased estimate.

What are quartiles and how are they calculated?

Quartiles divide a sorted dataset into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 (50th percentile) is the overall median, and Q3 (75th percentile) is the median of the upper half. The IQR (interquartile range) = Q3 − Q1 and is used to detect outliers.

How do I detect outliers using statistics?

The IQR method: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are considered outliers. The Z-score method: values more than 2 or 3 standard deviations from the mean are outliers. For small samples, the IQR method is more robust because it does not assume a normal distribution.

What does variance measure and how does it relate to standard deviation?

Variance measures the average squared deviation from the mean. Standard deviation is simply the square root of variance, which brings the measure back to the original units of your data. Variance is useful in formulas (e.g., ANOVA), but standard deviation is more intuitive for interpretation.