Statistics Calculator
Full descriptive statistics for any dataset - mean, median, mode, standard deviation, quartiles - plus a histogram and box plot drawn instantly.
Analyze
| Count | 8 |
| Mean (average) | 5.0000 |
| Median | 4.5000 |
| Mode | 4 |
| Standard deviation | 2.0000 |
| Variance | 4.0000 |
| Min / Max | 2 / 9 |
| Range | 7.0000 |
| Q1 / Q3 | 4.0000 / 5.5000 |
| IQR | 1.5000 |
| Sum | 40.0000 |
Histogram
Box plot
The box shows Q1 to Q3 with a line at the median; whiskers reach the min and max.
Mean, Median, Mode: Which Average?
The mean adds everything up and divides — familiar, but one billionaire in the room makes the "average" salary meaningless. The median is the middle value when sorted, so it ignores extremes: it's why house prices are usually reported as medians. The mode is the most frequent value, handy for categories like "most common shoe size." When all three agree, your data is nicely symmetric; when they disagree, the shape of the data is telling you something.
Reading the Spread
Two datasets can share a mean of 50 yet behave nothing alike: {48, 49, 50, 51, 52} versus {0, 0, 50, 100, 100}. Standard deviation and variance measure that difference — roughly, the typical distance from the mean. The interquartile range (IQR) does a similar job but only looks at the middle 50% of values, so outliers can't distort it. If your SD is large next to your mean, expect surprises.
What the Charts Tell You
The histogram shows the shape: a bell means symmetric, a long tail on one side means skew (income data almost always tails right). The box plot compresses the same story into five numbers — min, Q1, median, Q3, max. A median line off-center inside the box, or one whisker much longer than the other, confirms skew at a glance.
My saved numbers reuse them in any calculator
Save a number once — like your rent or hourly rate — then just type its name instead of the number, in any calculator here. You can also type formulas like 5000 * 1.1 right into any box.
Saved only in this browser — nothing is sent to us.
Frequently Asked Questions
What is the difference between mean, median and mode?
The mean is the sum divided by count; the median is the middle value when sorted; the mode is the most frequent value. The mean is sensitive to outliers, the median is not - that is why house prices use medians.
How do you find quartiles?
Sort the data, then find the medians of the halves: Q1 is the 25th percentile, Q3 the 75th. The middle 50% of values sit between them; the distance Q3 - Q1 is the interquartile range (IQR).
What does a box plot show?
Five numbers in one picture: min, Q1, median (the line inside the box), Q3, max. A median off-center in the box, or one long whisker, reveals skew instantly.
What is the interquartile range?
IQR = Q3 - Q1: the spread of the middle half of your data. Unlike standard deviation, outliers cannot distort it, which makes it the robust choice for skewed data.
When should I use sample instead of population?
Use sample when your data is a subset standing in for something larger (survey respondents, trial patients). It divides by N-1 instead of N, correcting the bias from estimating the mean from the data itself.