Average Calculator

This tool allows you to quickly and effortlessly calculate various measures of central tendency for a given set of numbers, including the arithmetic, geometric, and harmonic means.

How to Use

Input Numbers:

• Enter your numbers into the input fields. You can add more fields up to the total of 50 by clicking the "Add More" button.

Generate Results:

• Click the "Generate" button to calculate and display the following values:
  • Arithmetic Mean
  • Geometric Mean
  • Harmonic Mean
  • Median
  • Largest
  • Smallest
  • Range
  • Midrange

Description and Calculation Formulas

Arithmetic Mean:

Arithmetic mean, arithmetic average, or just the mean or average is calculated by summing all numbers in a set and dividing by the count of numbers in the set.

Arithmetic Mean = (x1 + x2 + x3 + … + xn) / n

For example: 
for numbers 2, 4, 5,  9, the arithmetic mean is (2 + 4 + 5 + 9) / 4 = 5

Corresponding Google Sheets / Excel function: =AVERAGE(range)

For more information see:  Arithmetic mean - Wikipedia

Geometric Mean:

The geometric mean of a set of n numbers is the nth root of the product of all  numbers in the set.

Geometric Mean = (x1 ×  x2 ×  x3 × … × xn)^(1 / n)

For example: 
for numbers 2, 4, 8, the geometric mean is (2 × 4 × 8)^(1/3) = 64^(1/3) = 4

Corresponding Google Sheets / Excel function: =GEOMEAN(range)

For more information see: Geometric mean - Wikipedia

Harmonic Mean:

The harmonic mean of a set of n numbers  is the size of the set n divided by the sum of the reciprocals of each of the numbers  in the set.

Harmonic Mean = n / (1/x1 + 1/x2 + 1/x3 + … + 1/xn)

For example: 
for numbers 2, 4, 8, 8, the harmonic mean is 4 / (1/2 + 1/4  + 1/8 + 1/8) = 4 / (8/8) =  4

Corresponding Google Sheets / Excel function: =HARMEAN(range)

For more information see: Harmonic mean - Wikipedia

Median:

The median of a set of numbers is the value that is greater than or equal to at least half of the items in the set and also is less than or equal to at least half of the numbers in the dataset. In other words, the median is the "middle" number in the dataset arranged in ascending order. If the data set contains an even number of values, the median is usually defined as the arithmetic mean of the two middle values.

For example: 
for numbers 1, 3, 4, 5, 7, the median is 4
for numbers 1, 3, 4, 5, 7, 8,  the median is 4.5

Corresponding Google Sheets / Excel function: =MEDIAN(range)

For more information see: Median - Wikipedia

Midrange:

The midrange is the average of the largest and smallest values in a set.

Midrange =  (xmin + xmax) / 2

For example:
for numbers 1, 3, 4, 5, 7, 8,  the midrange is (1 + 8) / 2 = 4.5

For more information see: Mid-range - Wikipedia

Range:

The range is the difference between the largest and smallest values in a set.

Range =  xmax - xmin

For example:
for numbers 1, 3, 4, 5, 7, 8,  the range is 8 -1 = 7

For more information see: Range (statistics) - Wikipedia