What is the difference between mean, median, and mode?

Mean is the arithmetic average: sum all values and divide by the count. Median is the middle value when data is sorted (or average of two middle values for even counts). Mode is the most frequently occurring value. For the dataset {2, 3, 3, 5, 7}: mean = 4, median = 3, mode = 3. Use median for skewed data (salaries, house prices) as it resists outliers.

What is standard deviation?

Standard deviation measures how spread out values are from the mean. Population std dev (sigma) divides by N; sample std dev (s) divides by N-1 for unbiased estimation. For {2, 4, 4, 4, 5, 5, 7, 9}: mean = 5, population std dev = 2, sample std dev = 2.14. About 68% of data falls within 1 std dev of the mean in a normal distribution.

When should I use population vs sample standard deviation?

Use population standard deviation (divide by N) when your data includes every member of the group you are studying. Use sample standard deviation (divide by N-1, Bessel's correction) when your data is a subset drawn from a larger population. Most real-world datasets are samples. Example: test scores of 30 students in a class of 30 = population; scores of 30 from a school of 500 = sample.

What are quartiles and IQR?

Quartiles divide sorted data into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 is the overall median (50th percentile), Q3 (75th percentile) is the median of the upper half. IQR (interquartile range) = Q3 - Q1, representing the middle 50% of data. Values below Q1 - 1.5*IQR or above Q3 + 1.5*IQR are considered outliers.

What do skewness and kurtosis tell me?

Skewness measures asymmetry: positive skew means a right tail (more low values), negative skew means a left tail (more high values), zero means symmetric. Kurtosis (excess) measures tail heaviness relative to a normal distribution: positive kurtosis means heavier tails (more outliers), negative means lighter tails, zero matches normal distribution. Income data typically has positive skew.

What is the coefficient of variation?

Coefficient of variation (CV) is the ratio of standard deviation to the mean, expressed as a percentage: CV = (std dev / |mean|) * 100%. It measures relative variability, allowing comparison between datasets with different units or scales. A CV of 10% means the standard deviation is 10% of the mean. Lower CV indicates more consistent data. Not meaningful when the mean is zero or near zero.

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Statistics Calculator

Descriptive statistics summarize a dataset. Central tendency: mean (arithmetic average), median (middle value), mode (most frequent). Dispersion: standard deviation (spread from mean), variance (std dev squared), range (max - min), IQR (Q3 - Q1). For {2, 4, 4, 4, 5, 5, 7, 9}: mean = 5, median = 4.5, mode = 4, population std dev = 2, sample std dev = 2.14.

Calculate mean, median, mode, standard deviation, variance, quartiles, IQR, skewness, kurtosis, and more from any dataset. Supports both population and sample statistics. Geometric and harmonic means included.

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How to Use

1
Enter your data
Type or paste numbers separated by commas, spaces, or newlines. Minimum 2 values required. Use presets (Test Scores, Temperatures, Stock Returns) for quick testing.
2
Review central tendency
See mean (average), median (middle value), and mode (most frequent value). For skewed data, median is more representative than mean.
3
Analyze dispersion
Check standard deviation (spread), variance, range, IQR (middle 50%), and coefficient of variation. Both population and sample statistics are shown.
4
Check distribution shape
Skewness indicates asymmetry (positive = right tail, negative = left tail). Kurtosis indicates tail heaviness relative to normal distribution.

Frequently Asked Questions

What is the difference between mean, median, and mode?: Mean is the arithmetic average: sum all values and divide by the count. Median is the middle value when data is sorted (or average of two middle values for even counts). Mode is the most frequently occurring value. For the dataset {2, 3, 3, 5, 7}: mean = 4, median = 3, mode = 3. Use median for skewed data (salaries, house prices) as it resists outliers.
What is standard deviation?: Standard deviation measures how spread out values are from the mean. Population std dev (sigma) divides by N; sample std dev (s) divides by N-1 for unbiased estimation. For {2, 4, 4, 4, 5, 5, 7, 9}: mean = 5, population std dev = 2, sample std dev = 2.14. About 68% of data falls within 1 std dev of the mean in a normal distribution.
When should I use population vs sample standard deviation?: Use population standard deviation (divide by N) when your data includes every member of the group you are studying. Use sample standard deviation (divide by N-1, Bessel's correction) when your data is a subset drawn from a larger population. Most real-world datasets are samples. Example: test scores of 30 students in a class of 30 = population; scores of 30 from a school of 500 = sample.
What are quartiles and IQR?: Quartiles divide sorted data into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 is the overall median (50th percentile), Q3 (75th percentile) is the median of the upper half. IQR (interquartile range) = Q3 - Q1, representing the middle 50% of data. Values below Q1 - 1.5*IQR or above Q3 + 1.5*IQR are considered outliers.
What do skewness and kurtosis tell me?: Skewness measures asymmetry: positive skew means a right tail (more low values), negative skew means a left tail (more high values), zero means symmetric. Kurtosis (excess) measures tail heaviness relative to a normal distribution: positive kurtosis means heavier tails (more outliers), negative means lighter tails, zero matches normal distribution. Income data typically has positive skew.
What is the coefficient of variation?: Coefficient of variation (CV) is the ratio of standard deviation to the mean, expressed as a percentage: CV = (std dev / |mean|) * 100%. It measures relative variability, allowing comparison between datasets with different units or scales. A CV of 10% means the standard deviation is 10% of the mean. Lower CV indicates more consistent data. Not meaningful when the mean is zero or near zero.

Common Statistical Measures

Measure	Formula	Use Case	Sensitive to Outliers
Mean	Sum / N	General average	Yes
Median	Middle value when sorted	Skewed data (income, prices)	No
Mode	Most frequent value	Categorical data	No
Std Dev (Pop)	sqrt(sum((x-mean)^2) / N)	Full population spread	Yes
Std Dev (Sample)	sqrt(sum((x-mean)^2) / (N-1))	Sample spread estimation	Yes
IQR	Q3 - Q1	Robust spread measure	No
CV	(Std Dev / \|Mean\|) * 100%	Compare variability across scales	Yes
Skewness	Third standardized moment	Distribution asymmetry	Yes

Statistics Calculator

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Common Statistical Measures

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