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

Mean is the sum divided by the count, median is the center of the sorted list, and mode is the most frequently occurring value or values.

What is the difference between population and sample standard deviation?

The population formula uses N when the data represents the complete group. The sample formula uses n−1 to correct estimation when the data represents part of a larger population.

What does standard deviation tell me?

Standard deviation shows how spread out values are around the mean. A smaller value means the data is more tightly grouped, while a larger value means it is more dispersed.

Can a data set have more than one mode?

Yes. If multiple values share the highest frequency, the calculator lists all of them as modes. If no value repeats, the data set has no mode.

What are Q1, Q2, and Q3?

Q1, Q2, and Q3 are quartiles near the 25th, 50th, and 75th percentiles. Q2 is also the median.

How is IQR calculated?

Interquartile range is Q3 minus Q1. It measures the spread of the middle 50 percent of the data.

Can standard deviation be calculated from one value?

A one-value population has a standard deviation of zero. Sample standard deviation is undefined because it requires at least two values.

Tools/🧮 Calculators/Statistics Calculator

Statistics Calculator

Calculate mean, median, mode, standard deviation, variance, range, quartiles, and IQR.

Version 1.0 · Last Updated: August 8, 2026 · Maintained by ToolLarder

How are basic statistics calculated?

The Statistics Calculator summarizes central tendency, spread, and quartile distribution in a single analysis. It automatically applies the appropriate variance and standard deviation formula for population or sample data.

Mean, median, and mode calculator

The mean combines every value, the median identifies the center of the sorted list, and the mode shows the most frequently occurring values.

Mean = Σx ÷ n

Standard deviation and variance

Variance measures squared distance from the mean, while standard deviation is its square root expressed in the same unit as the data.

σ = √(Σ(x − μ)² ÷ N)

Population vs. sample standard deviation

Use N when analyzing the complete population and n−1 when a sample is being used to estimate a larger population.

Sample variance = Σ(x − x̄)² ÷ (n − 1)

Q1, Q2, Q3, and IQR calculator

Quartiles divide sorted data into four parts. IQR measures the width of the middle 50 percent and is resistant to extreme values.

IQR = Q3 − Q1

Range, minimum, and maximum

Minimum and maximum identify the data boundaries. Range is the difference between the largest and smallest values.

Range = Maximum − Minimum

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