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Descriptive Statistics Calculator
Paste in a list of numbers and get every key statistic at once. Each result comes with a plain explanation, so you understand what the number means, not just what it is.
Please enter at least two numbers to get a full result.
Count
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Sum
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Mean
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Median
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Mode
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Range
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Minimum
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Maximum
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Variance (sample)
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Std deviation (sample)
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Q1 (25th pct)
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Q3 (75th pct)
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Box plot: how your data is spread
How often each value appears
Understand each statistic
Tap any statistic below to see its formula, what it means, and a real life example. This helps you use these numbers with real confidence.
Mean (Average)
Mean = Sum of all values ÷ Count of values
Add up every number in your list. Then divide that total by how many numbers you have. That gives you the mean.
Why you need it: the mean gives you one simple number that represents your whole data set. It is the most common way to describe a typical value.
Example: you spend $40, $55, and $30 on groceries in three separate weeks. Your mean weekly spend is $125 divided by 3, which is about $41.67.
Median
Median = the middle value once sorted
Sort every number from smallest to largest. If there is an odd count, the middle number is your median. If there is an even count, average the two middle numbers.
Why you need it: the median is not affected by extreme values. It often shows a truer typical value than the mean when your data has outliers.
Example: five houses on a street sell for $200k, $210k, $215k, $220k, and $900k. The median price is $215k, which is far more useful than the mean here.
Mode
Mode = the value that appears most often
Count how many times each number shows up. Whichever number repeats the most is the mode. A data set can have one mode, several, or none at all.
Why you need it: the mode tells you the most common result, which is useful when you care about frequency rather than an average.
Example: a shoe store sells sizes 8, 9, 9, 10, 9, and 11 in one day. Size 9 is the mode, since it sold the most times.
Range
Range = Maximum value minus Minimum value
Find the largest number and the smallest number in your data. Subtract the smallest from the largest. That difference is the range.
Why you need it: range gives you a fast, simple sense of how spread out your data is, from lowest to highest.
Example: daily temperatures this week hit a low of 61 and a high of 84. The range is 23 degrees.
Variance
Variance = Average of squared differences from the mean
For each number, find how far it is from the mean, then square that distance. Average all those squared distances together. That average is the variance.
Why you need it: variance measures how much your numbers spread out around the mean. A bigger variance means more spread and less consistency.
Example: two delivery drivers both average 30 minutes per trip. One driver is always close to 30. The other swings between 10 and 50. The second driver has much higher variance.
Standard Deviation
Standard deviation = Square root of variance
Take the variance you just calculated and find its square root. This brings the number back into the same units as your original data.
Why you need it: standard deviation is the most common way to describe consistency. A small number means your data sits close to the mean.
Example: a factory machine cuts parts averaging 10cm long with a standard deviation of 0.1cm. That is a tight, reliable process worth trusting.
Quartiles & Interquartile Range
IQR = Q3 minus Q1
Sort your data and split it into four equal parts. Q1 is the value a quarter of the way through. Q3 is the value three quarters of the way through. IQR is the gap between them.
Why you need it: the IQR focuses on the middle 50% of your data, ignoring extreme outliers at either end.
Example: most employees at a small company earn between the 25th and 75th pay percentile. That middle range is far more useful than the full min to max spread.
Frequently asked questions
What is the difference between sample and population statistics?
A population includes every possible data point. A sample is a smaller group taken from that population. Sample formulas divide by count minus one, which slightly adjusts for using an incomplete data set.
What does a high standard deviation actually mean?
It means your values are spread far from the mean, showing more inconsistency. A low standard deviation means your values cluster tightly around the mean.
Why can a data set have more than one mode?
If two or more values tie for the highest frequency, each one counts as a mode. This is called being bimodal or multimodal.
Should I use the mean or the median for my data?
Use the median when your data has outliers, like income or house prices. Use the mean when your data is fairly even, without extreme highs or lows.
Want to put these numbers to work?
Try the Compound Interest Calculator next.
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