5 questions
Statistics & Probability
Distributions, estimators, expected values and hypothesis tests with clear derivations.
standard deviation 3variance 2descriptive statistics 2probability 2linear transformation 1normal distribution 1z score 1quartiles 1histogram 1grouped data 1kernel methods 1linear algebra 1gaussian processes 1numerical analysis 1dice 1
Calculators
Quartiles
Find Q1, median, Q3 and IQR from a list of values or from histogram bins (grouped data), with every step shown.
Standard deviation
Sample and population standard deviation, variance and mean, with the full sum-of-squares working.
Normal probability
Given the mean and standard deviation, find P(X < b), P(X > a) or P(a < X < b) with z-scores.
Dice probability
Exact distribution, mean and standard deviation for the sum of any number of fair dice.
Questions
- Does Standard Deviation Change When You Add or Multiply by a Constant?Adding a constant leaves the standard deviation unchanged; multiplying by a scales it by |a| and the variance by a². Proof, examples and the general rule for aX + b.
- Given the Mean and Standard Deviation, How Do You Find a Probability?Convert values to z-scores and use the standard normal table to find P(X < b), P(X > a) and P(a < X < b) from a mean and standard deviation, with examples.
- How to Find Quartiles from a Histogram (Grouped Data)Find Q1, the median and Q3 from a histogram using cumulative frequencies and the grouped-data interpolation formula, with a fully worked example.
- Inverting a Gaussian (RBF) Kernel Matrix Without Numerical TroubleA Gaussian kernel matrix is positive definite for distinct points, so it is invertible, but it is often badly conditioned. Use a ridge term and a Cholesky solve instead.
- What Is the Standard Deviation of a Dice Roll?The standard deviation of one fair six-sided die is √(35/12) ≈ 1.708. See the derivation, the formula for any die, and how it scales for sums and averages.