About Statistics Calculator
Descriptive statistics summarise a dataset with key measures. Mean = sum of values divided by count. Median = middle value when sorted (resistant to outliers). Mode = most frequent value. Standard deviation measures spread around the mean; variance = standard deviation squared; range = max minus min.
When to use each: use mean for symmetric distributions; use median for skewed data like income or house prices where outliers distort the mean; use mode for categorical data. For normally distributed data, approximately 68% of values fall within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 (the empirical rule). Applications include quality control, investment risk analysis, scientific experiments, and survey data summarisation.
Enter coefficients for: ax² + bx + c = 0
About Quadratic Equation Solver
A quadratic equation has the form ax squared plus bx plus c equals zero. The quadratic formula x = (-b plus or minus square root of (b squared minus 4ac)) divided by 2a gives all solutions. The discriminant D = b squared minus 4ac determines solution type: D greater than 0 gives two distinct real roots; D equals 0 gives one repeated root; D less than 0 gives two complex roots.
Applications include projectile motion (finding time of flight), profit maximisation models, electrical circuit resonance, and geometry area problems. This solver shows the discriminant, both roots, vertex coordinates of the parabola, and axis of symmetry.
About Triangle Calculator
A triangle is fully determined by any three elements (sides or angles) where at least one is a side. Area = half times base times height. For two sides and included angle: Area = 0.5 times a times b times sin(C). For all three sides, use Heron's formula: Area = square root of s(s-a)(s-b)(s-c) where s is the semi-perimeter (perimeter divided by 2).
Law of Sines: a divided by sin(A) equals b divided by sin(B) equals c divided by sin(C) - use when you know two angles and a side. Law of Cosines: c squared = a squared plus b squared minus 2ab times cos(C) - use for two sides and included angle or all three sides known. Sum of all interior angles always equals 180 degrees. This tool handles all valid triangle configurations and shows all computed properties.
About Probability Calculator
Probability measures event likelihood on a scale of 0 (impossible) to 1 (certain). P(A) = favourable outcomes divided by total possible outcomes. Addition rule: P(A or B) = P(A) + P(B) minus P(A and B). Multiplication rule: P(A and B) = P(A) times P(B given A). Complement rule: P(not A) = 1 minus P(A).
Independent events have no effect on each other - past coin flips do not affect future ones, which is the gambler's fallacy. Conditional probability P(B given A) is the foundation of Bayes' theorem, which powers medical diagnostics, spam filtering, and machine learning. Applications include quality control defect rates, insurance actuarial calculations, genetics Punnett squares, game strategy, and financial risk modelling.
About Prime Number Checker
A prime number is divisible only by 1 and itself. To check if n is prime, test divisibility by all integers up to the square root of n - if none divide evenly, n is prime. This is efficient because if n has a factor larger than its square root, the complementary factor must be smaller than the square root.
Prime numbers are the building blocks of all integers - every integer greater than 1 is a unique product of primes (Fundamental Theorem of Arithmetic). Primes are essential in cryptography: RSA encryption relies on the computational difficulty of factoring the product of two very large prime numbers. There are infinitely many primes, as proved by Euclid around 300 BCE. The largest known prime numbers now contain over 40 million digits.
About Fraction Calculator
Fractions represent exact rational numbers - unlike decimals they never suffer from floating-point rounding errors. Addition and subtraction require finding the Least Common Denominator first, then combining numerators. Multiplication: multiply numerators together and denominators together. Division: multiply by the reciprocal of the second fraction (flip it).
Simplification divides both numerator and denominator by their Greatest Common Divisor (GCD). Mixed numbers like 2 and three-quarters convert to improper fractions by multiplying whole number by denominator and adding numerator (giving 11 over 4). Fractions are used in engineering tolerances, recipe scaling, probability calculations, music time signatures, and construction measurements. This calculator shows all working steps.
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About Logarithm and Exponential Calculator
Logarithms and exponentials are inverse operations. Log base b of x equals y means b raised to y equals x. Common logarithm uses base 10; natural logarithm ln(x) uses base e (approximately 2.71828). Key identities: log(a times b) = log(a) + log(b); log(a divided by b) = log(a) minus log(b); log(a to the n) = n times log(a).
The exponential growth model A = A0 times e to the rt is used for population growth, continuously compounded interest, radioactive decay, and epidemic modelling. Decibels in audio use log base 10. pH in chemistry = negative log of hydrogen ion concentration. The Richter earthquake scale uses log base 10. The natural log derivative equals 1 over x, making it fundamental in calculus and solving differential equations.