Free Average Calculator: Mean, Median and Range

What Does the Average Calculator Do?

Quick answer: An average calculator finds the arithmetic mean, which is your numbers added together and divided by how many there are. Enter your numbers in the fields above, at least two of them, then press Generate and read the Result card.

One press of Generate fills eight rows, each with its own copy icon: Count, Average, Geometric Mean, Harmonic Mean, Median, Largest, Smallest and Range. The Median row sits beside the Average, so one page works as a mean calculator and a median calculator.

Up front, one limit: every number counts equally and there is no weight field, so a weighted mean is a by-hand job, covered below.

How to Use the Average Calculator

1. Enter your numbers. Four fields are open on arrival, each showing #: as its placeholder. Type one number per field. Whole numbers, negatives, one or two decimals and scientific notation such as 1e3 all go in, and a blank field stops the form in the browser.
2. Add or remove fields. Add More adds one field per click, up to 50 fields. The red cross beside a field removes one you do not need, and the last two stay because at least two numbers are required. After removing a field and adding one back, check your values: in our tests the new field's cross removed an older one.
3. Press Generate. The page reloads with a Result card under the form, and your numbers stay in the fields.
4. Read and copy the results. The copy icon beside a row copies that one value.

Typo check: If a result looks odd, read Largest and Smallest first, because an extra digit, such as 920 for 92, shows up there. Fix it, then try your own numbers again.

A Worked Example With Real Numbers

Take five test scores: 85, 90, 78, 92 and 88. By hand, 85 + 90 + 78 + 92 + 88 = 433, and 433 divided by 5 is 86.6. Six of the eight checks fit on paper, while the geometric and harmonic rows need a scientific calculator.

The tool stops at PHP's 14 significant digits and leaves rounding to you, so shorten the two long decimals yourself (86.46 and 86.31, rounded). For positive numbers the means keep a fixed order: average, then geometric, then harmonic, tying only when every value matches.

Enter the same five numbers and your Result card should match the table row for row.

What Each Result Means

Start with Count, Average and Median. Treat the page as a geometric mean calculator or harmonic mean calculator only for growth factors and rates.

The Pythagorean means article explains why that order holds. The spread between the three rows is a rough gauge of how uneven a list is: 30, 32, 35, 38 and 400 gave 107, 55.16 and 40.99 in our tests (rounded).

How to Calculate an Average by Hand

Here is how to find the average of a set of numbers on paper: count the values, add them, then divide the total by that count. That is the whole average formula.

average = sum of values ÷ number of values

Whole numbers first: 12 + 15 + 21 = 48, and 48 ÷ 3 = 16. Decimals behave the same, so 0.5 and 0.25 total 0.75, which halves to 0.375. A negative just pulls the total down, so -4, -2 and -6 sum to -12, and -12 ÷ 3 = -4. The calculator returned 0.375 and -4 for those last two.

Knowing how to calculate average figures by hand lets you audit any result. Do the sum on paper, press Generate and compare, and if the two disagree, check Count first.

Units and groups: Keep one unit throughout, and think twice before averaging two averages. If 2 scores average 90 and 8 average 70, the plain average of 90 and 70 is 80, but all ten scores average (180 + 560) ÷ 10 = 74, because the bigger group should count for more.

Average vs Median vs Mode: Which One Should You Use?

Try 30, 32, 35, 38 and 400: the Average comes back as 107 and the Median as 35. The 400 is an outlier, a value far from the rest of the data set, so the mean lands where none of the five numbers is. Four of the five values sit between 30 and 38, so 35 describes the typical value and 107 describes nobody.

Average, median and mode are the usual measures of central tendency in descriptive statistics. To find a median, sort the list, then take the middle value for an odd count or the mean of the two middle values for an even one, so 2, 4, 4, 4, 5, 5, 7, 9 gives (4 + 5) ÷ 2 = 4.5. The Measures of the Center of the Data chapter of OpenStax Introductory Statistics covers both cases, and the NIST handbook on measures of location gives the formula.

The mode is the most frequent value. In that same set 4 appears three times, so one list gives three answers: average 5, median 4.5, mode 4. A set can have several modes (1, 2, 2, 3, 3, 4 has two) or none. The Result card has no mode row, so sort the list and count repeats yourself.

Rule of thumb: Use the average when values sit close together, and check the median whenever the list holds extreme values.

How to Find a Weighted Average

This calculator gives every number the same pull and has no weight field. A weighted average, or weighted mean, changes the recipe: multiply each value by its weight, add the products, then divide by the total of the weights.

Say homework scored 92 at 20 percent, a quiz 80 at 30 percent and the exam 85 at 50 percent. Then 0.2 × 92 + 0.3 × 80 + 0.5 × 85 = 18.4 + 24 + 42.5 = 84.9. Enter 92, 80 and 85 and the Average reads 85.666666666667 (85.67 rounded), because each score weighs the same. That 0.77 gap is what the weights are worth.

Weights tip: Decimal weights that add up to 1 need no final division; otherwise divide by their total. Divide a percent weight by 100 to get a decimal, so 20 percent is 0.2. The percentage calculator and the guide on how to calculate a percentage cover the rest.

Tips, Limits and Edge Cases

Five limits, roughly in the order you will meet them.

• Size. You start with four fields, Add More reaches 50 fields in all, and at least two numbers are required. At 50 fields, Add More stays on screen and does nothing.
• Decimals. The number boxes use a step of 0.01, so the browser refuses a value like 1.005. Results carry up to 14 significant digits as PHP prints them, so floating-point noise can show: 0.1, 0.2 and -0.3 average 1.8503717077086E-17, not 0. Read that as zero.
• Zero and negatives. Average, Median, Largest, Smallest and Range accept both: -4, -2 and -6 give an average of -4 and a range of 4. A negative leaves the Geometric Mean and Harmonic Mean rows reading not defined. A zero does the same to the Harmonic Mean, as do reciprocals that cancel, such as 1 and -1, while the other rows still fill in.
• Missing features. There is no mode row, no weights, no moving average and no step-by-step workings. With no box for pasting a list, 40 numbers means 36 clicks on Add More.
• Stale tabs. A tab left open for a long time can answer Generate with four empty fields and a notice. Type the numbers in again.

Where an Average Calculator Comes in Handy

An average of numbers calculator pays off on small jobs, where a few numbers need one figure to stand for them.

• Grades and surveys. Average a term of test scores or a set of survey results.
• Sales and expenses. Average weekly sales figures, order values or a year of monthly bills.
• Website traffic. Enter a week of daily visits, or the page load time from five test runs, then read the Median beside the Average so one slow run stands out.
• Measurements. Average a week of temperature readings or points per game.

Free to Use, No Account Needed

This free average calculator needs no account to run, and there is nothing to install. Everything happens on one page: press Generate and the page reloads with the Result card.

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