Statistics Calculator

Find the descriptive summary statistics for a set of data by entering the numbers below. Keep reading to learn how to calculate each one.

Separate numbers using a comma (,)
Separate numbers using a comma (,)

Results:

Min:
 
Max:
 
Count:
 
Range:
 
Sum:
 
Mean:
 
Median:
 
Mode:
 
Standard Deviation:
 
Variance:
 
Sum of Squares:
 
Quartile Q1:
 
Quartile Q2:
 
Quartile Q3:
 
Interquartile Range:
 
Midrange:
 
Mean Absolute Deviation:
 
Geometric Mean:
 
Coefficient of Variation:
 
Relative Standard Deviation:
 


How to Find the Minimum Value

The minimum value is the smallest number in the set. To find the minimum value, start by ordering the numbers from smallest to largest, then simply find the smallest number.

How to Find the Maximum Value

The maximum value is the largest number in the set. Just like finding the minimum value, start by sorting the numbers from smallest to largest, then find the largest number.

How to Find the Count

The count is the size of the data set and is often denoted as n. To find the count, simply count the number of elements in the set.

How to Find the Range

The range is the difference between the minimum value and the maximum value in the data.

R = H – L

Where:
R = range
H = highest number
L = lowest number

How to Find the Sum

The sum is the value of each number in the set added together. To find the sum, add up each number to find the total.

You can also use a tool like our mean, median, mode calculator to find the sum automatically.

How to Find the Mean

The mean is the average value of a set of numbers and is a measure of the central tendency of the data.

x̄ = ∑xi ÷ n

Where:
x̄ = mean
xi = each number in the set
n = count

How to Find the Median

The median is the middle value in the data set. The median is also a measure of the central tendency of the data.

To find the median, order the data from smallest to largest, then find the middle value in the set. If the number of values in the set is even, then the median is equal to the mean of the middle two values.

How to Find the Mode

The mode is the value that occurs most often in the data set. It is possible for a data set to have no modes, which can occur when no value repeats more than once. It’s also possible to have multiple modes, where multiple values repeat the same number of times.

To find the mode, document the frequency that each value occurs in the data. The mode will be the number with the greatest frequency of occurrence.

How to Find the Standard Deviation

The standard deviation is a measure of the distribution or variance between numbers in a data set.

graphic showing the standard deviation formula where sigma is equal to the square root of the sum of squares divided by N

How to Find the Variance

The variance is the measure of the variability from the mean in a data set. The variance is equal to the standard deviation squared.

graphic showing the variance formula where sigma squared is equal to the sum of squares divided by N

How to Find the Sum of Squares

The sum of squares is a measure of the deviation from the mean for numbers in a data set. It’s often used to calculate variance and standard deviation.

SS = ∑(xi – x̄)²

How to Find the Quartiles

Quartiles mark the boundaries or divisions of a data set into four equally sized groups. Each quartile is a median of a portion of the dataset.

The first quartile is the median of the lower half of the data, while the third quartile is the median of the upper half.

How to Find the Interquartile Range

The interquartile range is the difference between the first and third quartiles.

IQR = Q3 – Q1

Where:
IQR = interquartile range
Q1 = first quartile
Q3 = third quartile

How to Find the Midrange

The midrange is the arithmetic mean of the smallest and largest numbers in a data set.

M = H + L2

Where:
M = midrange
H = highest number
L = lowest number

How to Find the Mean Absolute Deviation

The mean absolute deviation is the average difference between each value in the set and the mean.

graphic showing the mean absolute deviation-formula formula where the MAD is equal to the sum of the absolute value of the difference between each number in the set and the mean, divided by the count of numbers in the set

Where:
xi = each number in the set
x̄ = the mean
n = size of the set

How to Find the Geometric Mean

The geometric mean is the average of a data set that is found using the nth root of the product of each number in the set, where n is the size of the set.

graphic showing the geometric mean formula where the geometric mean is equal to the nth root of the product of all numbers in the set, where n is the count of numbers in the set

Where:
xi = each number in the set
n = number of elements in the set

How to Find the Coefficient of Variation

The coefficient of variation is a measure of relative variability or dispersion of data around the mean in a sample or population.

CV = σμ

Where:
CV = coefficient of variation
σ = standard deviation
μ = mean

How to Find the Relative Standard Deviation

The relative standard deviation is a measure of how closely the data is clustered around the mean in a sample or population.

RSD = |σμ|

Where:
RSD = relative standard deviation
σ = standard deviation
μ = mean