π Statistics Calculator
Enter numbers to get complete descriptive statistics.
Mean
Median
Std Dev (s)
How to Use This Calculator
Paste or type your numbers into the text area, separated by commas or spaces. The calculator accepts any set of two or more numbers and returns the full set of descriptive statistics at once, including both sample and population standard deviation.
Enter your dataset. You can type numbers one per line, separated by commas, or separated by spaces. Example: 4, 8, 15, 16, 23, 42.
Click Calculate. Results update automatically as you type.
Read the three headline values at the top: Mean, Median, and Sample Standard Deviation. These three together give a quick summary of any dataset.
Scroll through the full results for Q1, Q2, Q3, IQR, variance, range, min, max, and the sorted data list.
Key Statistics Formulas
Use sample standard deviation (divides by n-1) when your data is a sample from a larger population. Use population standard deviation (divides by n) only when you have data on every member of the full population. For most practical purposes, the sample version (s) is the right choice.
Worked Examples
Where This Comes Up in Real Life
Quality control in manufacturing uses standard deviation to monitor whether a production process is staying within tolerance. If a factory produces 10 mm bolts and the sample standard deviation of diameters is 0.05 mm, then using the empirical rule (68-95-99.7), about 99.7% of bolts will fall within 3 Γ 0.05 = 0.15 mm of the target. If the tolerance is Β±0.1 mm, roughly 4.5% of bolts will be out of spec and need to be caught by inspection.
Comparing mean to median quickly reveals skew in a dataset. House prices in a city might have a mean of Β£350,000 but a median of Β£280,000. The mean is dragged up by a small number of very expensive properties. The median better represents what a typical buyer pays. This distinction matters in economics, health research, and any field where a few extreme values could mislead a simple average.
Frequently Asked Questions
What is the difference between mean and median?
The mean is the average (sum Γ· count). The median is the middle value when sorted. For skewed data, the median is more representative. Example: [1, 2, 3, 4, 100] β mean=22, median=3.
What is standard deviation?
Standard deviation measures the spread of data around the mean. A low SD means data points are clustered near the mean; high SD means they're spread out. It's the square root of variance.
What is the difference between population and sample standard deviation?
Population SD divides by N (all members known). Sample SD divides by Nβ1 (Bessel's correction) to give an unbiased estimate when you're working with a sample from a larger population.
What are quartiles?
Quartiles divide sorted data into four equal parts. Q1 (25th percentile), Q2 (50th, = median), Q3 (75th percentile). The interquartile range (IQR) = Q3 β Q1.
What is the mode?
The mode is the most frequently occurring value in a dataset. A dataset can be bimodal (two modes) or multimodal. If all values occur once, there is no mode.