Statistics Calculator

What is a Statistics Calculator?

A statistics calculator takes a list of numbers and instantly works out the key descriptive statistics that summarise the data: how many values there are, their sum, the mean (average), the median (middle value), the mode (most common value), the range, the variance and the standard deviation, plus the quartiles. These measures answer two basic questions about any data set — where is its centre, and how spread out is it? Students meet them in every statistics course, and they are used everywhere from grading and finance to science and quality control. This tool also draws a histogram so you can see the shape of the distribution at a glance, and it reports both the population and the sample versions of variance and standard deviation so you can pick the right one for your situation.

How to use this calculator

1. Type or paste your numbers into the box. You can separate them with commas, spaces or new lines. 2. The results update instantly as you type — no button to press. 3. Read the headline measures (count, sum, mean, median, mode, range, min, max) at the top. 4. Check the variance and standard deviation table, choosing the population or sample column to match your data, and read the quartiles and interquartile range below the histogram.

The formulas behind the numbers

Mean: x̄ = (Σx) / n — the sum of all values divided by how many there are. Median: the middle value of the sorted data (or the average of the two middle values when n is even). Mode: the value that appears most often. Range: max − min. Population variance: σ² = Σ(x − x̄)² / n. Sample variance: s² = Σ(x − x̄)² / (n − 1). Standard deviation is the square root of the variance: σ = √σ² (population) or s = √s² (sample). Quartiles Q1 and Q3 are found by linear interpolation, and the interquartile range is IQR = Q3 − Q1. For the data set 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the median is 4.5, the mode is 4, the population standard deviation is 2 and the sample standard deviation is about 2.138.

Reading your results

The mean and median both describe the centre of your data. When they are close, the data is fairly symmetric; when the mean is pulled away from the median, outliers or a skew are at work. The standard deviation tells you how far, on average, values sit from the mean — a small value means the data is tightly clustered, a large one means it is spread out. The key choice is population versus sample: divide by n when your numbers are the entire group you care about, and by n − 1 when they are a sample used to estimate a bigger population. The quartiles and the interquartile range (IQR) describe the middle 50% of the data and are useful for spotting outliers, which often lie more than 1.5 × IQR beyond Q1 or Q3.

Frequently Asked Questions