Statistics Calculator
Enter a list of numbers to instantly compute 13 descriptive statistics: mean, median, mode, standard deviation, variance, quartiles, IQR, range, min, max, count, and sum.
Last updated: March 2026
How to Use the Statistics Calculator
- Enter your data in the text area. Use commas, spaces, or line breaks to separate values. Example:
4, 8, 15, 16, 23, 42 - Results update instantly — all 13 statistics appear the moment you type.
- Review the sorted data list below the calculator to see how your values rank, making quartile positions easy to verify.
- Share or clear using the buttons below the input area.
Measures of Central Tendency Explained
Descriptive statistics summarize a dataset with a few key numbers. The three most fundamental measures are the mean, median, and mode — each tells a different story about the "center" of the data.
Mean (Arithmetic Average)
The mean is the sum of all values divided by the count. It uses every value in the dataset and is sensitive to extreme values (outliers). Best used for symmetric distributions without extreme values — like heights, weights, or test scores in a controlled group.
Median
The median is the middle value when data is sorted in order. For an even count, it is the average of the two middle values. The median is resistant to outliers — adding a value of 1,000,000 to a dataset barely moves the median but massively changes the mean. Best used for skewed data like incomes, house prices, and wait times.
Mode
The mode is the value that appears most frequently. A dataset can have no mode (all values unique), one mode (unimodal), two modes (bimodal), or many modes (multimodal). Especially useful for categorical data: the most popular product color, the most common survey answer, or the most frequent error code.
Measures of Spread: Range, IQR, and Standard Deviation
Central tendency tells you where data is centered. Spread tells you how consistent or variable the data is. Three key spread measures are complementary:
- Range (Max − Min): The simplest spread measure, but highly sensitive to extreme outliers. A single unusually high or low value can make the range misleading.
- Interquartile Range (IQR = Q3 − Q1): Measures the spread of the middle 50% of data. Robust against outliers. Used to define outlier thresholds: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are potential outliers (Tukey's fences).
- Standard Deviation: Measures average distance from the mean. Uses all values, so it's influenced by outliers but provides a comprehensive picture of spread. Used in z-scores, confidence intervals, and the normal distribution.
When Data is Skewed
In a right-skewed distribution (long tail on the right, e.g., income data), mean > median > mode. In a left-skewed distribution (long tail on the left), mean < median < mode. When mean and median are close, the data is roughly symmetric. Use this relationship to quickly assess the shape of your distribution.
Using Statistics to Detect Outliers
The IQR method identifies potential outliers: compute Q1 − 1.5×IQR (lower fence) and Q3 + 1.5×IQR (upper fence). Any value outside these fences is a potential outlier. For example, with Q1 = 10, Q3 = 20, IQR = 10: lower fence = −5, upper fence = 35. A value of 80 would be flagged as an outlier.
How to Calculate Statistics If...
What is the mean, median, and mode of 2, 3, 5, 7, 9?
Mean = 5.2, Median = 5, Mode = none (no repeating values). Sum = 26, n = 5, mean = 5.2. Sorted: 2, 3, 5, 7, 9 — middle value is 5. All values appear once, so there is no mode.
What if there are two modes in a dataset?
The dataset is bimodal — both values are listed as modes. For {1, 2, 2, 3, 4, 4, 5}, both 2 and 4 appear twice, making it bimodal. This calculator displays all modes separated by commas.
What is the IQR of 1, 3, 5, 7, 9, 11, 13?
The IQR is 8. Sorted: 1, 3, 5, 7, 9, 11, 13. Median = 7. Lower half: {1, 3, 5} → Q1 = 3. Upper half: {9, 11, 13} → Q3 = 11. IQR = Q3 − Q1 = 11 − 3 = 8.
What is the median of an even number of data points?
The median is the average of the two middle values. For {2, 4, 6, 8}, the two middle values are 4 and 6, so median = (4 + 6) / 2 = 5.
How does an outlier affect the mean vs. the median?
Outliers strongly affect the mean but barely affect the median. Dataset {10, 10, 10, 10, 1000}: mean = 208, median = 10. The single extreme value pulls the mean far from where most data lies, but the median correctly represents the typical value.
What is the five-number summary of 3, 7, 8, 5, 12, 14, 21, 13, 18?
Sorted: 3, 5, 7, 8, 12, 13, 14, 18, 21. Min = 3, Q1 = 6, Median = 12, Q3 = 16, Max = 21. The five-number summary is {3, 6, 12, 16, 21}.
What does a high standard deviation relative to the mean indicate?
When SD is large relative to the mean, the data has high variability (coefficient of variation CV = SD/mean). A CV > 30% indicates high relative variability. This is common in financial data, biological measurements, and survey responses on subjective questions.
How do I find the mode of a dataset with no repeating values?
If no value repeats, there is no mode. The mode is only defined when at least one value appears more than once. This calculator displays "No mode" in that case.
What is the variance of {4, 7, 13, 16}?
Mean = 10. Sample variance ≈ 30.67. Deviations: −6, −3, 3, 6. Squared: 36, 9, 9, 36. SS = 90. Sample variance = 90 / 3 = 30. SD = √30 ≈ 5.48.
Can I use this for grouped frequency data?
This calculator works on raw data — individual values, not frequency tables. To use frequency data, expand it: if value 5 appears 3 times, enter 5, 5, 5. For large frequency tables, use a dedicated grouped data statistics tool.
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This calculator shows all computed statistics simultaneously, and the sorted data list lets you verify median and quartile positions step by step. Enter your data set and instantly see mean, median, and all modes. For a full step-by-step SD calculation, use the Standard Deviation Calculator which shows every deviation and squared difference.
How to find Q1 and Q3 quartiles
Sort the data, find the median, then find the median of the lower half (Q1) and upper half (Q3). For {2, 4, 6, 8, 10, 12}: Median = 7. Lower half {2, 4, 6} → Q1 = 4. Upper half {8, 10, 12} → Q3 = 10. IQR = 10 − 4 = 6. Different textbooks and software may use slightly different quartile calculation methods.
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Descriptive statistics summarize a dataset with measures of center (mean, median, mode) and spread (range, IQR, standard deviation). This tool computes all of them instantly — ideal for statistics courses, homework assignments, and exam preparation. The sorted data display helps students understand how quartiles are derived.
Statistics calculator for standard deviation and variance
This calculator computes sample standard deviation and variance alongside all other descriptive statistics. It uses the N−1 (Bessel's correction) formula for both, appropriate for sample data. For population statistics, use the Standard Deviation Calculator which lets you switch between sample and population formulas.
How to identify outliers in a data set
Use Tukey's fences: an outlier is any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR. Get Q1, Q3, and IQR from this calculator, then compute the fences manually. Extreme outliers use a factor of 3×IQR. Visual methods like box plots also clearly show outliers.
Difference between descriptive and inferential statistics
Descriptive statistics summarize the data you have (mean, SD, range); inferential statistics use that data to make predictions about a larger population (confidence intervals, hypothesis tests). This is a descriptive statistics calculator. Inferential statistics require additional assumptions about the population distribution and usually involve t-tests, ANOVA, or regression.
Frequently Asked Questions
What is the mean, median, and mode of 2, 3, 5, 7, 9?
Mean = 5.2, Median = 5, Mode = none (no values repeat). Range = 7, Min = 2, Max = 9.
What happens if there is no mode?
If all values in a dataset appear exactly once, there is no mode. The calculator displays "No mode" in this case. A dataset can also be bimodal (two modes) or multimodal (three or more).
What is the IQR used for?
IQR (Q3 − Q1) measures the spread of the middle 50% of data. It is used to assess variability, compare distributions, and identify potential outliers (values more than 1.5×IQR beyond Q1 or Q3).
What is the five-number summary?
The five-number summary is: Minimum, Q1, Median, Q3, Maximum. It compactly describes a distribution and forms the basis of a box plot. This calculator shows all five values.
Does this calculator show population or sample statistics?
Standard deviation and variance are computed using sample formulas (N−1). For population formulas, use the dedicated Standard Deviation Calculator where you can switch between the two.
How is the median calculated for even-count data?
When the count is even, the median is the average of the two middle values after sorting. For {2, 4, 6, 8}, median = (4 + 6) / 2 = 5.
When should I use the mean vs. the median?
Use mean for symmetric data without extreme outliers. Use median when data is skewed or contains outliers (e.g., income, property prices). The median is more representative when a few extreme values are present.
What data formats are accepted?
Numbers separated by commas, spaces, or line breaks. Negative numbers and decimals are supported. Non-numeric characters are ignored.
What is the difference between range and IQR?
Range = Max − Min (total span of all data). IQR = Q3 − Q1 (span of the middle 50%). Range is sensitive to outliers; IQR is not. Use IQR when outliers may be present.
Is my data private?
Yes — all computations run entirely in your browser. No data is sent to any server or stored anywhere.
What does bimodal mean in statistics?
Bimodal means the dataset has two modes — two values that each appear more frequently than all others. For example, {1, 2, 2, 3, 4, 4, 5} has modes 2 and 4. Bimodal distributions often indicate two distinct sub-groups within the data.