CalcLibrary

Statistics Calculator

Calculate mean, median, mode, standard deviation, variance, range, and more from a list of numbers. Enter comma-separated values.

Examples

Statistics for 85, 90, 78, 92, 88

Mean (Average)
86.6
Median
88
Standard Deviation
4.882622
Mode
No mode
Range
14
Variance
23.84
Count
5
Sum
433
Minimum
78
Maximum
92

Roughly symmetric distribution — mean (86.60) and median (88.00) are close.

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Examples

How It Works

Formula

xˉ=1n∑i=1nxi\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i

σ2=1n∑i=1n(xi−xˉ)2\sigma^2 = \frac{1}{n}\sum_{i=1}^{n} (x_i - \bar{x})^2

σ=σ2\sigma = \sqrt{\sigma^2}

Range=xmax⁡−xmin⁡\text{Range} = x_{\max} - x_{\min}

Variables

xix_i

The i-th value in the data set

nn

Number of values (the count)

xˉ\bar{x}

Mean (arithmetic average) of the data set

σ2\sigma^2

Population variance

σ\sigma

Population standard deviation

xmin⁡,  xmax⁡x_{\min},\; x_{\max}

Smallest and largest values in the data set

Enter numbers separated by commas. The calculator sorts them and computes: mean (sum/count), median (middle value), mode (most frequent), variance (average squared deviation from mean), standard deviation (square root of variance), range (max - min).

Frequently Asked Questions

01What is the mean?
The mean (arithmetic average) is the sum of all values divided by the count. It measures the central tendency of a data set.
02What is the median?
The median is the middle value when data is sorted. For even counts, it is the average of the two middle values. It is less affected by outliers than the mean.
03What is the mode?
The mode is the value that appears most frequently. A data set can have no mode (all values unique), one mode, or multiple modes.
04What is standard deviation?
Standard deviation measures how spread out values are from the mean. A low value means data points cluster near the mean; a high value means they are spread widely.
05Is this population or sample variance?
This calculator uses population variance (divides by N). For sample variance, divide by N-1 instead. The difference matters mainly for small samples.

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