Statistics Calculator - AnyCalcOnline

This statistics calculator helps you analyze data sets by calculating common statistical measures such as mean, median, mode, range, variance, standard deviation, and more. It also provides probability calculations and correlation analysis.

How the Statistics Calculator Works

Descriptive Statistics

The descriptive statistics calculator analyzes a set of data values to provide various statistical measures:

Central Tendency Measures: Mean (average), median (middle value), and mode (most frequent value)
Dispersion Measures: Range, variance, and standard deviation
Other Measures: Count, sum, minimum, and maximum values

Calculation Methods:

Mean: The sum of all values divided by the number of values.

Mean = (x₁ + x₂ + ... + xₙ) / n

Median: The middle value when data is sorted. For an even number of values, it's the average of the two middle values.

Mode: The value that appears most frequently. There may be no mode or multiple modes.

Range: The difference between the maximum and minimum values.

Range = Max - Min

Variance: The average of squared differences from the mean.

Variance = Σ(x - Mean)² / n

Standard Deviation: The square root of the variance.

Standard Deviation = √Variance

Probability Calculator

The probability calculator computes probabilities for different probability distributions:

Binomial Distribution

Used when there are exactly two possible outcomes ("success" and "failure") for each trial.

P(X = x) = (n choose x) × p^x × (1-p)^(n-x)

Where:

n = number of trials
x = number of successes
p = probability of success on a single trial
(n choose x) = n! / [x! × (n-x)!]

Normal Distribution

Used for continuous data that follows a bell-shaped curve.

P(X ≤ x) = Φ((x - μ) / σ)

Where:

μ = mean
σ = standard deviation
Φ = cumulative distribution function of the standard normal distribution

Poisson Distribution

Used for counting the number of events in a fixed interval of time or space.

P(X = x) = (λ^x × e^(-λ)) / x!

Where:

λ = mean rate of events
e = base of natural logarithm (approximately 2.71828)
x = number of events

Correlation Calculator

The correlation calculator analyzes the relationship between two sets of data (X and Y values).

Pearson Correlation Coefficient

Measures the strength and direction of the linear relationship between two variables.

r = Σ((x - x̄)(y - ȳ)) / √[Σ(x - x̄)² × Σ(y - ȳ)²]

Where:

x̄ = mean of X values
ȳ = mean of Y values

The correlation coefficient ranges from -1 to 1:

r = 1: Perfect positive correlation
r = 0: No correlation
r = -1: Perfect negative correlation

Linear Regression

Finds the best-fitting straight line through the data points.

y = mx + b

Where:

m = slope = Σ((x - x̄)(y - ȳ)) / Σ(x - x̄)²
b = y-intercept = ȳ - m × x̄