Statistics Calculator

Calculate statistical measures including mean, median, mode, standard deviation, and probability.

Analysis Type

Data Input

Data Values

Enter numbers separated by commas (e.g., 1, 2, 3, 4, 5)

Sample Datasets

Key Formulas

Mean: x̄ = Σx / n

Std Dev: s = √(Σ(x-x̄)² / (n-1))

Correlation: r = Σ(x-x̄)(y-ȳ) / √(Σ(x-x̄)²Σ(y-ȳ)²)

t-test: t = (x̄-μ) / (s/√n)

Descriptive Statistics

Mean

Median

Std Dev

6.0553

Count

Min

Max

Range

Q1

6.5

Q3

15.5

Skewness

Normal

Kurtosis

-1.2

Mesokurtic

Data Quality: Good

Completeness: 1.0%

Step-by-Step Analysis

1Data: [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] (n = 10)

2Mean (μ): Sum of all values / n = 11.0000

3Median: Middle value when sorted = 11.0000

4Standard deviation (σ): √(Σ(x-μ)²/(n-1)) = 6.0553

5Range: Max - Min = 20 - 2 = 18

6Quartiles: Q1 = 6.50, Q3 = 15.50, IQR = 9.00

How it works

A statistics calculator summarizes a data set with measures of center (mean, median, mode) and spread (range, variance, standard deviation). Together they describe where the data sits and how scattered it is.

Core statistics

Mean = Σx ÷ n        Range = max − min        Variance = Σ(x − mean)² ÷ n

Σx: sum of all values
n: count of values
mean: the average

Worked example

Data: 2, 4, 4, 6, 9

Mean = 25 ÷ 5 = 5
Median (middle) = 4, Mode = 4
Range = 9 − 2 = 7

Mean 5, median 4, mode 4, range 7.

Good to know

The mean is sensitive to outliers; the median resists them and is better for skewed data.
Standard deviation (the square root of variance) reports spread in the data's original units.
Use the sample variance (÷ n−1) when your data is a sample of a larger population.

Related Calculators

Frequently Asked Questions

When should I use the mean, median, or mode?

Use the mean for symmetric data without outliers, the median for skewed data like incomes or home prices, and the mode for categorical data where you want the most common value.

How do I spot outliers in a data set?

A standard test flags values more than 1.5 x IQR below the first quartile or above the third quartile. Alternatively, z-scores beyond about ±3 mark points far outside the typical range.

What is a z-score?

A z-score standardizes a value: z = (x - mean) / standard deviation. It tells you how many standard deviations a point sits from the mean, making values from different scales directly comparable.

What do range and interquartile range tell me?

Range (max - min) shows total spread but is hypersensitive to a single extreme value. The IQR — the span of the middle 50% of data — is a robust spread measure that outliers barely move.

How do I interpret a confidence interval?

A 95% confidence interval means that if you repeated the sampling process many times, about 95% of the intervals built this way would contain the true population value. It quantifies the uncertainty in your estimate.