Combinatorics and Error Calculators
This page presents tools that generate counts for item selections and summarise numerical differences between predicted and observed values across datasets.
-
Combination and Permutation Calculator
The counting of ordered and unordered selections shows how many possible outcomes arise when choosing from a fixed set of items.
Example use: Working out how many different snack selections can be made when choosing a few items from a small bowl.
Inputs: select calculation type, total number of items, number to choose, allow repetition
Outputs: total outcomes, probability, information entropy, visualised outcomes
Visual: a set of bars showing how the number of possible outcomes changes as the number of chosen items varies
-
Mean Absolute Error Calculator
The comparison between observed values and predicted values highlights how far the predictions differ from the actual results on average.
Example use: Checking how closely guessed step counts match the actual number recorded during a short walk.
Inputs: observed values, predicted values
Outputs: number of pairs, mean absolute error, total absolute error, root mean square error, error variance, error skewness, error kurtosis
Visual: a display comparing observed and predicted points, along with a view of how the absolute differences are spread out
-
Mean Absolute Percentage Error Calculator
The comparison of observed and predicted values in percentage terms shows how large the typical proportional difference is between the two sets.
Example use: Checking how far estimated cooking times differ from the actual times taken for a simple meal.
Inputs: observed values, predicted values
Outputs: mean absolute percentage error, standard deviation of percentage errors, error range, skewness, kurtosis
Visual: a set of points showing observed and predicted values, along with percentage differences from a perfect match line
-
Mean Squared Error Calculator
The squared differences between observed and predicted values provide a measure of how strongly the predictions deviate from the actual results.
Example use: Comparing how far estimated room temperatures differ from the temperatures actually measured during a day.
Inputs: observed values, predicted values
Outputs: total sum of squared errors, mean squared error, root mean squared error, error variance, error skewness, error kurtosis
Visual: a comparison of observed and predicted points showing how closely the two sets align
-
Root Mean Squared Error Calculator
The square-rooted average of squared differences between observed and predicted values gives a single measure of typical deviation.
Example use: Checking how far estimated journey times differ from the actual time taken to walk a familiar route.
Inputs: observed values, predicted values
Outputs: root mean squared error, mean squared error, mean absolute error, sum of squared errors, standard deviation of residuals, residual skewness, residual kurtosis
Visual: a comparison of observed and predicted points, along with a view showing how the residual differences vary across the index of observations
-
Standard Error Calculator
The standard error estimates how close your sample mean is likely to be to the true population mean, based on the spread of your sample and its size.
Example use: Estimating how close your calculated average reading speed is to your true long-term average.
Inputs: select input type, sample data, standard deviation, sample size, mean, confidence level
Outputs: standard error, mean, sample size, standard deviation, margin of error, confidence interval
Visual: a scatter of sample points with lines marking the mean and the upper and lower confidence limits
Combinatorics and Error Calculators FAQs
A permutation counts arrangements where order affects the result, while a combination counts selections where order has no influence.
MSE squares prediction differences before averaging, increasing the impact of larger errors, whereas MAE uses absolute values directly to summarise overall deviation.
A high MAPE value reflects a larger proportional difference between predicted and actual values across the dataset.
Standard error summarises how much sample means vary around a central value, indicating expected fluctuation across repeated samples.