Author: Luc Hens.
Version: 20 December 2021
The WolframAlpha web page (link) is the front end of a knowledge engine that (among many other things) is a powerful and user-friendly statistical calculator. On a smartphone or tablet use the mobile version in a browser, or the WolframAlpha app or the Wolfram Statistics Course Assistant app (about €2-3 each). Below are some examples of WolframAlpha input to do some basic statistical calculations. More examples here.
| What you want to find | WolframAlpha input |
|---|---|
| descriptive statistics of a list {2, 2, 4, 5, 7} | {2, 2, 4, 5, 7} |
| mean of a list | mean {2, 2, 4, 5, 7} |
| median of a list | median {2, 2, 4, 5, 7} |
| standard deviation of a population (σ) | population standard deviation {2, 2, 4, 5, 7} |
| standard deviation of a sample (s ) | sample standard deviation {2, 2, 4, 5, 7} |
| probability density of the normal distribution | standard normal distribution |
| area under the normal curve between two values | P[-infinity < x < 1] |
| area under the Student t curve between two values | P[-infinity < x < 1] for x ~ Student's t distribution with 12 degrees of freedom |
| area under the Chi-square (χ2) curve between two values | P[3 < x < infinity] for x ~ chisquare distribution with 12 degrees of freedom |
| area under the F curve between two values (n = degrees of freedom in numerator; m = degrees of freedom in denominator) | P[3 < x < infinity] for x ~ F distribution with n = 5 and m = 2 |
| binomial distribution: probability of two successes in three trials with a probability of succes of 1/6 (k = 2, n = 3, p = 1/6) | probability of 2 successes in 3 trials with p=1/6 |
| roll a die | roll a die |
| roll a die (alt.) | RandomChoice[{1,2,3,4,5,6}] |
| roll two dice | roll 2 six-sided dice |
| flip a coin | flip a coin |
| flip a coin (alt.) | RandomChoice[{'heads','tails'}] |
| flip two coins | flip 2 coins |
| confidence interval for a population proportion (only for large random samples) | confidence interval for a population proportion |
| confidence interval for a population mean (only for large random samples) | confidence interval for a population mean |
| hypothesis test for a population proportion | one proportion hypothesis test |
| hypothesis test for a population mean | one mean hypothesis test |
| hypothesis test for two population proportions | two proportions hypothesis test |
| hypothesis test for two population means | two means hypothesis test |
| sample size | sample size |
| scatter plot and line of best fit through (1.3, 2.2),(2.1, 5.8),(3.7, 10.2), (4.2, 11.8) | linear fit {1.3, 2.2},{2.1, 5.8},{3.7, 10.2},{4.2, 11.8} |