Standard deviation, ratio and quadratic calculator●
Standard deviation, ratios, quadratic equations and greatest common divisor, each with the working shown.
Pick a calculator, then type your numbers. The result updates as you type. Nothing leaves this page.
Enter the numbers for a x² + b x + c = 0. The value a cannot be 0.
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How these four maths calculators work
Standard deviation measures how spread out numbers are around their mean. Subtract the mean from each value, square the differences, add them up and divide: by n for a whole population (σ) or by n - 1 for a sample (s). The square root of the result is the standard deviation, and before the square root it is the variance. For the numbers 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is exactly 2. A ratio compares quantities: to simplify it, divide every part by their greatest common divisor, so 12 : 18 becomes 2 : 3. To solve A : B = C : x, use x = B x C / A, and to share an amount, give each part its fraction of the total. A quadratic equation a x² + b x + c = 0 is solved with x = (-b ± √(b² - 4ac)) / 2a. The discriminant b² - 4ac tells you the roots: positive means two real roots, zero means one repeated root and negative means two complex roots. The greatest common divisor (GCD) is the largest number that divides all your numbers, found with Euclid's algorithm. The least common multiple (LCM) of two numbers is their product divided by their GCD.
Average calculator →Common questions
What is the difference between sample and population standard deviation?
Use population (divide by n) when your numbers are every value in the group. Use sample (divide by n - 1) when they are only part of a bigger group. The sample version is a little larger and is the usual choice.
How do I calculate standard deviation by hand?
Find the mean, subtract it from each number, square each difference, add the squares, divide by n or n - 1, then take the square root.
How do I simplify a ratio?
Divide every part by their greatest common divisor. For 12 : 18 the divisor is 6, so the ratio is 2 : 3. Decimals are scaled up to whole numbers first.
How do I solve a proportion such as 2 : 3 = 10 : x?
Multiply the middle terms and divide by the first: x = 3 x 10 / 2 = 15. Choose Find the missing number to do it automatically.
What does the discriminant tell me?
It is b² - 4ac. Above zero there are two real solutions, equal to zero there is one repeated solution, and below zero there are no real solutions, only complex ones.
How do GCD and LCM relate?
For two numbers, GCD x LCM equals the product of the numbers. The GCD is the biggest number that divides both and the LCM is the smallest number both divide into.
Is my information stored?
No. The numbers stay in your browser tab and are never sent or saved.