Statistics Calculator

Everything the calculator gives you

Enter your numbers once and read the whole table at a glance:

• Count and sum — how many values, and what they add up to.
• Central tendency — mean, median and mode, plus the geometric mean for values that compound.
• Spread — largest, smallest and range, then the standard deviation and variance for both a population (σ, σ²) and a sample (s, s²).
• Your data, sorted — printed under the table, so you can see the shape of it.
• Quartiles — Q1, Q3 and the interquartile range, under their own heading.

Two ways in, and they stay separate

The keypad at the top is for numbers that arrive one at a time — readings you are taking, marks you are reading off a page. Type a value, press ADD, and it joins the data set on the right; then press any statistic to read it back. Each key shows its name under its symbol, and you can remove a single value with the × beside it rather than clearing everything.

The comma-separated box below is for a list you already have. Type or paste your values separated by commas, spaces or line breaks — you can mix them, and blank entries are ignored. One Calculate returns the whole table at once, and it updates as you edit, so correcting a typo does not mean starting again.

The two keep their own data. Adding values on the keypad never changes what the box below reports, and vice versa.

One difference from most keypads worth knowing: if you have typed a number but not pressed ADD, pressing a statistic will tell you so rather than answering. A number on the screen is not in the data set until you add it, and a statistic for a set you did not mean to have is worse than no statistic.

A worked example you can check

For the data set 10, 2, 38, 23, 38, 23, 21, 23 the calculator reports a count of 8, a sum of 178, a mean of 22.25 and a median of 23. The mode is 23, appeared 3 times. The largest value is 38, the smallest is 2, and the range is 36. The geometric mean is 17.119851726053. The population standard deviation is 11.508149286484 with a variance of 132.4375; the sample standard deviation is 12.302729081677 with a variance of 151.35714285714. Sorted, the data reads 2, 10, 21, 23, 23, 23, 38, 38.

The geometric mean

The ordinary (arithmetic) mean adds your values and divides; the geometric mean multiplies them and takes the nth root. That makes it the right average whenever the quantities compound rather than accumulate — annual growth rates, investment returns, ratios, index numbers. It is never larger than the arithmetic mean, and it is only defined when every value is positive, so the calculator says the answer is undefined rather than printing a number for a set containing zero or a negative.

Mean, median and mode — a worked example

Take the data set 2, 3, 3, 5, 12:

• Mean = (2 + 3 + 3 + 5 + 12) ÷ 5 = 25 ÷ 5 = 5
• Median = the middle value of the sorted list = 3
• Mode = the most frequent value = 3 (it appears twice)
• Range = 12 − 2 = 10

Notice the mean (5) is higher than the median (3): the single large value, 12, pulls the average up while the median barely moves. That gap is a quick signal that the data is skewed.

When to use each measure

Measure	Best for
Mean	Roughly symmetric data with no extreme outliers
Median	Skewed data or data with outliers (incomes, prices)
Mode	The most common category or most frequent value

The five-number summary and quartiles

The five-number summary describes the data by position: minimum, first quartile (Q1), median, third quartile (Q3) and maximum. For the set 2, 3, 3, 5, 12 the median (3) splits it, and the quartiles are the medians of the halves on either side — Q1 is the median of the lower pair 2 and 3 = 2.5, and Q3 is the median of the upper pair 5 and 12 = 8.5. The interquartile range, Q3 − Q1 = 8.5 − 2.5 = 6, captures the middle half of the data.

Variance and standard deviation

For the same five values, each deviation from the mean of 5 squared and summed gives 66. Divide by N = 5 for the population variance of 13.2 (σ ≈ 3.63), or by N − 1 = 4 for the sample variance of 16.5 (s ≈ 4.06). These measure spread as an average distance from the mean, complementing the position-based interquartile range above. For the full step-by-step method and the population-vs-sample distinction, see the standard deviation calculator.

A note on quartiles

Quartiles here use the median-of-halves method (Tukey's hinges), excluding the overall median from each half when the count is odd. This is the convention taught in most introductory courses; some spreadsheet functions interpolate and can give slightly different Q1/Q3 values on small data sets. For percentages of a whole, the percentage calculator helps, and the scientific calculator handles individual formulas.