Average Tool
Calculate six types of averages from numerical data, including weighted and trimmed means. Review median, mode, dispersion, quartiles, outliers and frequency counts, with interactive histograms, box plots and downloadable results for further analysis.
| Value | Count | Frequency |
|---|
Table of Contents
Highlights
- Six average methods, including weighted and trimmed means
- Interactive histogram, box plot and observation chart
- Median, mode, quartiles and dispersion statistics
- Adjustable precision, histogram bins and variance type
- Export results as CSV or JSON and charts as PNG
How Average Tool Works?
An average summarises a set of numerical observations. The arithmetic mean divides their sum by the observation count, while other means emphasise different properties of the data. Enter values separated by commas, spaces, semicolons or line breaks, then select an average type.
| Average type | Definition | When useful |
|---|---|---|
| Arithmetic | Sum of observations divided by count | Ordinary numerical observations |
| Weighted | Sum of value × weight divided by total weight | Observations with unequal importance |
| Geometric | nth root of the product of positive observations | Multiplicative factors |
| Harmonic | Count divided by the sum of reciprocals of positive observations | Rates measured on a common basis |
| Trimmed | Arithmetic mean after removing observations from both sorted tails | Reducing the influence of extremes |
| Root mean square | Square root of the mean of squared observations | Magnitude of varying signals |
For the weighted mean, supply one non-negative weight per value and a positive total weight. Geometric and harmonic means require all values to be strictly positive. Trimming removes the selected percentage from each tail, rounded down to a whole number of observations.
Additional outputs include the median, repeated-value modes, minimum, maximum, range, quartiles, interquartile range (IQR), variance, standard deviation, standard error and coefficient of variation. Sample variance uses n − 1; population variance uses n. Quartiles use linear interpolation between sorted observations, and outliers are flagged below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. The histogram shows grouped frequencies, the box plot illustrates the five-number summary, and the values chart follows input order.
Practical Use Cases
Students: Compare an arithmetic mean with the median for assignment marks, then use the sample standard deviation to describe how widely results vary.
Teachers: Enter class scores, inspect the histogram for clustering and use a trimmed mean to see how unusually low or high scores influence the summary.
Business analysts: Assign weights to regional performance figures, then inspect the frequency table and quartiles to compare observations.
Investors: Explore geometric averages of positive growth factors and compare them with arithmetic averages when analysing compounded changes.
Engineers: Use root mean square for signed measurements where both positive and negative deviations contribute to overall magnitude.
Researchers: Switch between sample and population variance, review standard error and identify observations outside the 1.5 × IQR fences.
Accuracy and Limitations
Calculations use JavaScript floating-point numbers, so very large or extreme values can lose precision. Inputs are limited to 10,000 finite numbers; weighted means require matching non-negative weights, and geometric and harmonic means accept only positive data. Sample variance and standard error are unavailable for a single observation. Quartiles use linear interpolation, modes are omitted if every value occurs once, and IQR outlier flags are descriptive rather than proof of errors. Display rounding follows the selected decimal places. The values chart samples 1,000 points when the dataset is larger.
