Average Calculator

Average calculator at a glance#

What is the average of a set of numbers?#

The average, or arithmetic mean, is calculated by summing the numbers and dividing by the count of numbers. For the quiz scores 85, 72, 90, 88, and 95, you sum them to get 430. There are 5 scores, so the average is 430 ÷ 5, which is 86.

How do I use the average calculator?#

Enter your numbers into the box above, separating each one with a comma like this: 85, 72, 90, 88, 95. The calculator will display the average, as well as the sum, count, largest and smallest numbers, the median, the range, and the geometric mean. You can include decimals and negative numbers too.

What is the average of 40 and 100?#

To find the average of 40 and 100, add them to get 140, then divide by 2. The result is 70. The average will always be halfway between the two numbers, meaning 70 is 30 more than 40 and 30 less than 100.

What an average tells you#

An average helps you understand how much each item would get if the total were evenly distributed. The five quiz scores add up to 430 points. Distributing these points over five quizzes gives each one 86.

This concept makes the average a balance point. Three scores exceed 86: 90 is 4 points above, 88 is 2 above, and 95 is 9 above, totaling 15 points. Meanwhile, two scores fall short: 85 is 1 point short, and 72 is 14 short, also 15 in total. The amounts above and below the average always balance out, whatever numbers you begin with.

An average doesn't have to match any of your numbers. For instance, nobody scored 86 in a single quiz here, and an average might be a decimal, like 3.5 for the numbers 3 and 4.

How to calculate an average by hand#

You can find an average for any list of numbers by following three simple steps:

1. Add all the numbers together: 85 + 72 + 90 + 88 + 95 = 430.
2. Count how many numbers there are in the list: 5.
3. Divide the total sum by the count: 430 ÷ 5 = 86.

As a formula, average = sum ÷ count. You can add the numbers in any order, and the order you type them into the calculator won't change the result.

Average of two or three numbers#

When you're working with two numbers, add them together and divide by 2. For example, the average of 86 and 93 is calculated as 179 ÷ 2 = 89.5. With three numbers, you'll divide the sum by 3. So if you have 4, 8, and 12, they will average out to 24 ÷ 3 = 8. If the division gives a decimal, round it off at the end. For instance, 59, 73, and 83 add up to 215, and when you divide 215 by 3, you get 71.67 to two decimal places.

Averages with decimals and negative numbers#

Decimals follow the same process. Five lab readings of 63.3, 58.0, 64.6, 59.4, and 62.2 add up to 307.5, and then 307.5 divided by 5 is 61.5.

Negative numbers work similarly, as they are values below zero and reduce the sum. Four morning temperatures of −3, 2, 5, and −1 degrees total 3, leading to an average of 3 ÷ 4 = 0.75 degrees. Just type the minus sign before the number, and the calculator handles the rest.

Average per day, week or month#

A daily average represents the total for a period divided by the number of days within it. Imagine you tracked your food expenses for a week: $42, $18, $35, $60, $25, $12, and $46. The week's total comes to $238, and $238 ÷ 7 gives $34 per day.

You must count every day in the period, even days when you didn't spend anything. If nothing was spent on a day, enter 0 for it. Excluding a zero means dividing the same total by fewer days, which leads to an inflated average. This method applies equally to average sales per month, steps per day, or hours per week.

How to combine two averages#

Averaging two averages only works when both groups have the same number of values. Here's a common question: the average of 4 numbers is 12, and the average of 8 other numbers is 18. What is the average for all 12 numbers?

Using (12 + 18) ÷ 2 = 15 is incorrect, as the second group contains twice as many numbers. Instead, refer back to the totals:

• The total for the first group is 4 × 12 = 48.
• The second group totals 8 × 18 = 144.
• All 12 numbers total 48 + 144 = 192, and 192 ÷ 12 = 16.

The result, 16, is nearer to 18 because a greater portion of the numbers came from that group.

Weighted averages and grades#

This calculator counts every number once, which works well for a simple list. However, many grade averages assign more weight to certain scores. If your final exam holds twice the weight of your homework average, you can adjust by entering the exam score twice. For example, a homework average of 80 and an exam score of 90 are entered as 80, 90, and 90, which averages to 86.67.

When weights are specified as percentages, such as homework 20% and exams 50%, the grade calculator applies each score with its respective weight. To calculate a grade point average across different classes, use the GPA calculator.

What the other results mean#

In addition to the average, the calculator provides several other numbers about your data. For the quiz scores 85, 72, 90, 88, and 95:

• Sum and count are the components of the average: 430 and 5.
• The largest and smallest values are 95 and 72, with the range being the difference between them, 95 − 72 = 23.
• The median is the central number once sorted. In order, the scores are 72, 85, 88, 90, 95, making the median 88.
• The geometric mean involves multiplying the 5 numbers together and finding the 5th root of the product, which gives about 85.63 here.

The geometric mean is useful for growth rates. If an investment increases by 10% one year and decreases by 5% the next, enter the growth factors 1.10 and 0.95. The geometric mean is around 1.0223, which is roughly 2.2% a year. The simple average of 10% and −5% is 2.5%, which exaggerates growth. The calculator shows n/a for the geometric mean if any number is negative.

Averages people often look up#

These pairs and lists come from questions people search for. Each average is the sum divided by the count.

Sources#

• NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.5.1: Measures of Location

Frequently asked questions#

Is the average the same as the mean?#

Yes. In everyday use, the average refers to the arithmetic mean: the sum divided by the count. The median and the mode are other ways to represent a typical value, and they can produce different results with the same set of numbers. The mean, median and mode calculator shows all three side by side. The NIST Engineering Statistics Handbook defines the mean as the sum of the data points divided by the number of data points.

How do you average percentages?#

You should average percentages directly only when each percentage is derived from the same total. If not, add up the parts and the wholes instead. For instance, if you scored 9 out of 10 on one test (90%) and 30 out of 50 on another (60%), your overall score is 39 out of 60, which is 65%. This is different from the 75% you would get by averaging 90 and 60 directly.

Can the average be higher than all of the numbers?#

No. The average will always be somewhere between the smallest and the largest number in the list. It equals them only when all numbers in the list are the same.

Do zeros count when you calculate an average?#

Yes. A zero is a value. It adds nothing to the sum but still increases the count by 1. The average of 5, 0, and 7 is 12 ÷ 3 = 4. However, the average of 5 and 7 alone would be 6.

How do I enter numbers in the average calculator?#

You should separate the numbers with commas, like 12, 15, 9.5, 20. Spaces after commas are acceptable, but using only spaces between numbers gives an error, so ensure there's a comma between each.

What's the difference between the average and the median?#

The average considers the size of every number, while the median is the middle number after sorting the list.