Average Calculator: Mean, Median, Mode, and Range
To calculate the average, add all numbers and divide the sum by the number of values. For 10, 20, and 30, the sum is 60 and the count is three, so the average is 20.
This calculator finds the arithmetic mean and also reports the median, mode, range, sum, count, minimum, maximum, quartiles, variance, and standard deviation. These additional results help explain the center and spread of the data rather than reducing the entire list to one number.
How to Use the Average Calculator
- Enter at least one number in the input box.
- Separate values with commas, spaces, semicolons, or line breaks.
- Select the number of decimal places to show.
- Choose whether to display the sorted number list.
- Press Calculate Average. Results change only after the button is pressed.
- Open Additional Statistics for quartiles, geometric and harmonic means, variance, and standard deviation.
The calculator accepts integers, decimals, and negative numbers. It rejects text and incomplete numeric values instead of silently ignoring them.
What Is an Average?
In everyday use, “average” usually means the arithmetic mean. Add every data point and divide by the number of data points. NIST identifies the mean, median, and mode as common descriptions of a central or typical value and notes that the mean is commonly called the average.[1]
The word average can also refer more broadly to measures of central tendency. The median and mode may describe a typical value better when data are skewed, contain extreme values, or repeat in meaningful ways.
How to Find the Average
Follow two steps:
- Add all the values.
- Divide the sum by the number of values.
Worked example
Find the average of 10, 15, 15, 20, and 40:
Count = 5
Average = 100 ÷ 5 = 20
The average does not have to be one of the entered values. It represents the equal-share value the group would have if the total were divided evenly.
Mean, Median, Mode, and Range
Mean
The mean is the sum divided by the count. It uses every number, which makes it informative but sensitive to unusually high or low values.
Median
The median is the middle value after sorting. For an odd count, it is the single middle number. For an even count, it is the mean of the two middle numbers.[1]
Mode
The mode is the most frequently occurring value. A list can have one mode, several modes, or no mode when all values occur equally often.[1]
Range
The range measures the distance from the smallest value to the largest:
How Outliers Affect the Average
Consider 10, 10, 12, 14, and 54. The mean is 20, even though four of the five values are 14 or lower. The unusually large value pulls the mean upward. The median is 12, which may describe the center more naturally for this list.
Neither result is automatically wrong. The mean answers what the equal share would be, while the median identifies the middle of the ordered data. Review both when salaries, home prices, response times, or other data contain extreme values.
Average of Decimals and Negative Numbers
Decimal and negative values use the same formula. For 2.5, 3.75, and 4.25, divide the sum of 10.5 by three to get 3.5. For −5, 0, and 8, divide the sum of three by three to get an average of one.
Rounding each input or intermediate step can change the final result. Keep the original precision during the calculation and round only the result when accuracy matters.
How to Average Percentages
A simple mean of percentages is appropriate only when each percentage has equal importance and a comparable base. The average of 80% and 90% is 85% when both values have equal weight.
If 80% came from a 10-question test and 90% came from a 100-question test, averaging the two percentages equally can be misleading. Combine the earned points and possible points or use the Weighted Mean Calculator. For percentage-specific work, use the Percentage Calculator.
Average vs. Weighted Average
An arithmetic average gives every value equal influence. A weighted average gives values different influence based on frequency, quantity, importance, credit hours, or allocation.
| Question | Average | Weighted average |
|---|---|---|
| Does each value count equally? | Yes | No |
| Separate weights required? | No | Yes |
| Typical use | Equivalent observations | Grades, quantities, frequencies, allocations |
| Formula denominator | Number of values | Sum of weights |
If every score has equal importance, use this Average Calculator. If a final exam is worth 50% while homework is worth 20%, use the Weighted Mean Calculator.
Grade Average vs. Weighted Grade
A simple grade average adds scores and divides by the number of scores. It works when every test or assignment counts equally. If assignments have different point totals or category weights, the correct course grade may require a weighted calculation.
Use the Grade Calculator for points, assignment categories, and target-grade planning. Use this page for an equal-weight numerical average.
Geometric and Harmonic Means
The geometric mean multiplies positive values and takes the appropriate root. It can be useful for multiplicative changes and growth factors, but it is undefined in this calculator when any value is zero or negative.
The harmonic mean is the count divided by the sum of reciprocals. It is often used for rates under specific equal-quantity conditions. It is undefined when a value is zero or when the reciprocal total is zero.
Variance, Standard Deviation, and Quartiles
Variance and standard deviation describe spread around the mean. Population formulas treat the entered list as the complete population. Sample formulas apply the n − 1 denominator and require at least two values.
The first quartile, Q1, marks the 25th percentile, while Q3 marks the 75th percentile. Their difference is the interquartile range. This calculator uses inclusive linear interpolation for quartiles, consistent with a common spreadsheet-style percentile method.
How to Calculate an Average in Excel
In Microsoft Excel, use the AVERAGE function for a range of cells:
=AVERAGE(A1:A10)
For nonadjacent cells:
=AVERAGE(A1,A3,A5)
Microsoft documents AVERAGE as the spreadsheet function for arithmetic means. Conditional alternatives include AVERAGEIF and AVERAGEIFS.[2]
Common Average Calculation Mistakes
- Dividing by the wrong count: Repeated values still count as separate observations.
- Ignoring zero: Zero is a valid number and affects both sum and count.
- Confusing mean and median: The mean uses the sum; the median uses ordered position.
- Dropping negative signs: Negative values reduce the sum.
- Averaging averages blindly: Group averages require weighting when group sizes differ.
- Using a simple mean for weighted grades: Different course weights need a weighted calculation.
- Rounding too early: Intermediate rounding can change the final answer.
- Assuming a list always has one mode: It may have several modes or no unique mode.
Frequently Asked Questions
How do you calculate the average?
Add all values and divide the sum by the number of values.
Is average the same as mean?
In ordinary numerical calculations, average usually refers to the arithmetic mean.
What is the average of 10, 20, and 30?
The sum is 60 and the count is three, so the average is 20.
Can an average be a decimal?
Yes. The sum may not divide evenly by the number of values, so the average can be a decimal.
Do repeated numbers count more than once?
Yes. Every entered observation counts, including repeated values.
What is the difference between average and median?
The average is the sum divided by the count. The median is the middle value after sorting.
How do you average percentages?
Use a simple mean only for equally weighted, comparable percentages. Otherwise combine the underlying totals or use a weighted mean.
Can I calculate an average with negative numbers?
Yes. Add the signed values and divide by the total number of values.