Statistics Calculator and Standard Deviation Calculator
Our statistics calculator gives the mean, median, mode, quartiles and outliers of any data set in one go. It also works as a standard deviation calculator, with sample and population results side by side. Paste your numbers to see every figure.
What a Statistics Calculator Shows
Descriptive statistics sum up a list of numbers with a few key figures. The mean and median describe the center, while the range and standard deviation describe the spread. Our statistics calculator reports all of them at once, plus the quartiles and any outliers. You can paste numbers straight from a spreadsheet or a lab sheet.
How to Use the Statistics Calculator
- Paste or type your numbers, separated by commas, spaces or new lines.
- Choose sample if your data is part of a larger group, or population if it covers everyone.
- Read the mean and standard deviation at the top, then the other results below.
Results update as you type, and the sorted list helps you catch typing mistakes. Quartiles follow the median of halves method used by TI-84 calculators. Other tools may use a different quartile rule, so small gaps in Q1 and Q3 are normal.
Mean Median Mode in Plain Words
The mean is the sum of the values divided by how many there are. The median is the middle value once the data is sorted, so one huge salary cannot drag it upward the way it drags the mean. The mode is the value that appears most often, and a data set can have one, several or none. Our tool lists every mode and also works as a median calculator for long lists.
How to Calculate Standard Deviation
Standard deviation measures the typical distance between each value and the mean. A small value means the data sits close together, while a large one means it is spread out. The steps below show how to calculate standard deviation by hand for 3, 5, 7, 9 and 11.
- Find the mean: 35 ÷ 5 = 7.
- Subtract the mean from each value to get −4, −2, 0, 2 and 4.
- Square each result to get 16, 4, 0, 4 and 16, which add up to 40.
- Divide by n − 1 for a sample (40 ÷ 4 = 10) or by n for a population (40 ÷ 5 = 8).
- Take the square root, which gives 3.1623 for a sample and 2.8284 for a population.
The value before the square root is the variance, so the same steps show how to calculate variance. Enter these five numbers in the standard deviation calculator above and you will see matching answers. Most reports quote the standard deviation because variance is in squared units.
Sample Standard Deviation vs Population
Use the population formula only when your data includes every member of the group, such as all 30 students in one class. When your numbers are a sample drawn from a bigger group, divide by n − 1 instead. This change, called Bessel's correction, stops the result from understating the true spread.
The sample figure is always a little larger than the population figure for the same data. Our standard deviation calculator shows both, with your chosen type in the main box. The gap shrinks as the data set grows.
Quartiles, IQR and Outliers
Q1 is the median of the lower half and Q3 is the median of the upper half. The interquartile range is Q3 minus Q1, and it covers the middle 50% of the data. Values more than 1.5 × IQR below Q1 or above Q3 are flagged as outliers.
Take the set 12, 13, 14, 15, 15, 16 and 48. Q1 is 13 and Q3 is 16, so the upper fence is 20.5 and 48 counts as an outlier. That single value moves the mean to 19 while the median stays at 15. Check whether an outlier is a real result or a typing error before you remove it.
A Worked Example With Test Scores
A teacher records eight test scores: 72, 85, 90, 66, 85, 78, 94 and 70. The statistics calculator gives a mean of 80, a median of 81.5, a mode of 85 and a range of 28. Treated as a sample, the standard deviation calculator shows 10.07 and a variance of 101.43.
If these eight students are the whole class, the population figure is 9.42 instead. Q1 is 71, Q3 is 87.5 and the IQR is 16.5, so no score is an outlier. The standard error of the mean is 3.56 and the coefficient of variation is 12.59%.
Reading the Results
- In a roughly bell shaped data set, about 68% of values fall within one standard deviation of the mean.
- A mean far above the median hints at a few very large values.
- The coefficient of variation compares spread between data sets with different units.
Finance teams use the standard deviation calculator idea to measure risk, since a stock with a wider spread of returns swings more. For a weighted average, try our Average Calculator. Our Percentage Calculator helps when you need to turn results into percentages.
Why Use Our Statistics Calculator
It covers the center, spread, quartiles and outliers of your data in one pass. It also doubles as a standard deviation calculator for sample or population data. Everything runs in your browser and nothing you paste is stored. Paste your data and get every result now.
Frequently asked questions
Is this statistics calculator free?
Yes, it is free with no sign up and no limit on the number of values.
Is it a mean median mode calculator too?
Yes, all three appear in the results for any list of numbers.
Which standard deviation calculator result should I use?
Use the sample result for data from a larger group and the population result when you have every member.
What is the sample standard deviation?
It is the spread of a sample, found by dividing the squared distances by n − 1.
Can I use it as a median calculator?
Yes, the median appears for any list you enter.
How to calculate variance quickly?
Square each distance from the mean, add them and divide by n − 1 or n.
What are descriptive statistics?
They are summary figures such as the mean, median and spread of a data set.
What does the interquartile range show?
It shows the spread of the middle half of your data.
Related calculators
Other tools people use alongside the statistics calculator.