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Author: akawak

free online calculators > Articles by: akawak

Studentized Range (Tukey’s) Distribution Calculators

Utilize this specialized calculator to simplify statistical analyses involving the Studentized Range Distribution: Studentized Range (Tukey’s) Distribution Calculator Studentized Range (Tukey’s) Distribution Calculator This calculator computes the CDF, an approximate PDF (via finite differences), estimated mean/variance, and generates random samples for Tukey’s studentized range distribution. Parameters: r = number of groups, v = degrees of […]

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Arcsine Distribution Calculators

Use the Arcsine Distribution Calculator to analyze data following an arcsine distribution. Understand the fundamentals of the arcsine distribution and perform accurate calculations with ease.” Arcsine Distribution Calculator The Arcsine distribution is a special case of the Beta distribution with parameters \( \frac{1}{2} \) and \( \frac{1}{2} \). Its PDF is given by: $$ f(x)=\frac{1}{\pi\sqrt{x(1-x)}},\quad […]

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Mean, Median, and Mode Calculator

Mean, Median, and Mode Calculator Mean, Median, and Mode Calculator Enter a series of numbers (separated by commas or spaces) to calculate the mean, median, and mode. Step 1: Enter Numbers Numbers: Separate numbers with commas or spaces. Calculate Results Mean: Median: Mode: Recalculate How It Works The mean is calculated as: $$ \text{Mean} = […]

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Normal Distribution Calculator

Our Normal Distribution Calculator is a free online tool that displays the probability distribution for the given data set Normal Distribution Calculator Normal Distribution Calculator Enter the parameters to compute the CDF, PDF, and generate a random sample. Mean, \( \mu \): Std. Deviation, \( \sigma \): Value, \( x \): Calculate Results CDF at \( […]

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Limit Calculator

Limit Calculator Limit Calculator Calculate the limit of a function \( f(x) \) as \( x \) approaches a value \( x_0 \). Using the numerical approximation: \[ \lim_{x\to x_0} f(x) \approx \frac{f(x_0-\epsilon) + f(x_0+\epsilon)}{2} \] with a small \(\epsilon\) (here, \(\epsilon = 10^{-6}\)). * Enter the function (in terms of x) and the value […]

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Multivariable Calculator

Multivariable Calculator Multivariable Calculator Enter a mathematical expression using variables and provide their values to evaluate the expression. * Example: Expression: 3*x + 2*y – z^2 and Variables: x=2, y=4, z=1 Step 1: Enter Your Expression and Variables Expression: Enter a valid mathematical expression (use `*` for multiplication and `^` for exponentiation as `z*z` instead […]

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Triangular Distribution Calculators

Use our Triangular Distribution Calculators to calculate the PDF, CDF, Mean, Mode, Median, Variance and generate sample Triangular Distribution Calculator Triangular Distribution Calculator For parameters \(a\) (lower bound), \(b\) (upper bound) and \(c\) (mode with \(a < c < b\)), the PDF is given by: $$ f(x) = \begin{cases} 0, & x < a \text{ […]

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Poisson Distribution Calculators

Use our Poisson Distribution Calculators to models the probability of a given number of events occurring within a fixed interval of time, given a constant mean rate of occurrence and independence between events.  Poisson Distribution Calculator For the Poisson distribution with rate parameter \( \lambda \) (where \( \lambda > 0 \)), the PMF is: […]

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Beta Distribution Calculators

Beta Distribution Calculator Beta Distribution Calculator For shape parameters \( \alpha \) and \( \beta \) (both > 0), the Beta distribution is defined on the interval \([0,1]\) with the PDF: $$ f(x;\alpha,\beta) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)}, \quad 0 \le x \le 1, $$ where \( B(\alpha,\beta)=\frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha+\beta)} \). Step 1: Enter Parameters \( \alpha \): Enter a […]

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Regression Calculator

Linear Regression Calculator Enter your x‑values and y‑values (separated by commas) to calculate the regression line: \( y = mx + b \) and the coefficient of determination \( R^2 \). Step 1: Enter Data x‑values (comma separated): 1, 2, 3, 4, 5 y‑values (comma separated): 2, 4, 5, 4, 5 Calculate Regression Regression Results […]

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