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

Mean is the average (sum ÷ count). Median is the middle value when sorted. Mode is the most frequent value. Example: 1, 2, 2, 3, 100 → Mean = 21.6, Median = 2, Mode = 2. Median and mode are more useful than mean when data has outliers.

What is standard deviation?

Standard deviation measures how spread out numbers are from the mean. Low std dev = data is close to the mean. High std dev = data is spread widely. Formula: √(Σ(x−mean)² / n). Sample std dev divides by n−1 (Bessel's correction) for unbiased estimation from a sample.

When should I use sample vs population standard deviation?

Population std dev (÷n): when you have data for EVERY member of the group. Sample std dev (÷n−1): when your data is a sample from a larger population — this is far more common. In Excel: STDEV() = sample, STDEVP() = population. In statistics courses, the sample version is almost always used.

What is IQR (interquartile range)?

IQR = Q3 − Q1. Q1 is the 25th percentile (median of lower half), Q3 is the 75th percentile (median of upper half). IQR represents the spread of the middle 50% of data. It's resistant to outliers, unlike range or standard deviation. Outlier rule: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR.

Statistics Calculator — Mean, Median, Mode, Standard Deviation

Statistics Calculator

Enter a list of numbers to calculate mean, median, mode, range, variance, standard deviation, and IQR in one click.

QUICK ANSWER

Mean = sum ÷ count. Median = middle value (sorted). Mode = most frequent. Std Dev = √variance. Use sample std dev (÷n−1) for data samples, population std dev (÷n) only when you have every data point. Excel's STDEV() = sample, STDEVP() = population.

Enter numbers (comma, space, or new line separated)

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How descriptive statistics differ by curriculum

The formulas look the same worldwide, but which formula is taught as "standard" varies by country:

Country / System	Default Std Dev	Calculator key
🇺🇸 US (AP Stats, SAT)	Sample (÷n−1)	Sx on TI-84
🇬🇧 UK (A-level)	Sample (÷n−1)	σn−1 on Casio
🇯🇵 Japan (高校)	Population (÷n)	σ on Casio FX
🇩🇪 Germany (Gymnasium)	Sample (÷n−1)	s on scientific calc
🇮🇳 India (CBSE/ISC)	Population (÷n)	σ on CASIO fx-82
🇨🇳 China (高中)	Population (÷n)	σn on Casio

This calculator shows both — sample and population — so you always get the right answer regardless of which system you're working with.

Common uses

STDEV in Excel/Sheets — Use our calculator to verify. Excel STDEV() = sample (÷n−1).
Normal distribution — 68% of data falls within 1 std dev of the mean, 95% within 2.
Outlier detection — Values beyond mean ± 3 std dev are outliers (Z-score method).
Box plots — Use Q1, median, Q3, and IQR values from this calculator.