Average Calculator

Paste any list of numbers — separated by commas, spaces, or new lines — and get the full picture instantly: mean, median, mode, range, standard deviation, minimum, maximum, count, and sum, plus the sorted list. Add optional weights to get a weighted average, the way exam grades and credit hours actually work.

What Is an Average?

When people say “average” they almost always mean the arithmetic mean: add the values, divide by how many there are. In statistics, though, “average” is a wider word that also covers the median (the middle value) and the mode (the most common value). The right one depends on your data, which is why this calculator gives you all three. The National Institute of Standards and Technology Engineering Statistics Handbook defines all three, and the Khan Academy statistics courses teach them with examples.

The classic case for choosing carefully is income. In a street where nine people earn $40,000 and one earns $400,000, the mean is $76,000 — a figure nobody on the street actually earns — while the median is $40,000, which describes the typical resident. Whenever a few extreme values pull the mean away from the bulk of the data, the median is the honest headline. The mode, meanwhile, answers a different question entirely: what is most common? For shoe sizes, exam marks, or survey answers, the mode is often the most useful number of all.

Mean, Median, Mode — When to Use Each

Standard deviation deserves a note: a low value means the numbers cluster tightly around the mean; a high value means they spread widely. Two classes can share a mean of 70 yet be completely different — one clustered at 68–72, the other spread from 40 to 100. The population version divides by n and describes the list itself; the sample version divides by n − 1 and estimates the wider population the list came from. For a full class or complete dataset, use population; for a sample, use sample.

Weighted Averages

Not all values count equally. A final exam worth 60% should move your grade more than a quiz worth 10%, and a 4-credit course counts more than a 1-credit course. The weighted mean handles this: multiply each value by its weight, add those products, and divide by the total weight. Enter weights in the second box, one per number, in the same order. A student scoring 90 (weight 3), 80 (weight 2), and 70 (weight 1) has a weighted mean of (270 + 160 + 70) ÷ 6 = 83.3, not the simple mean of 80. For grade point conversions, see the percentage calculator for marks-to-percent work and the fraction calculator for fractional weights.

Tips for Reading Your Results

• Check the sorted list first. Outliers and typos jump out immediately — a stray 1000 among tens is usually a data-entry error.
• Report mean and median together. When they disagree, the gap itself tells you the data is skewed, and in which direction.
• There can be two modes. If two values tie for most frequent, the data is bimodal — both are reported above.
• Range is fragile. One extreme value stretches it, so pair it with standard deviation for a sturdier picture of spread.
• Round at the end. Keep full precision through the calculation and round only the displayed results.

A Full Worked Example: Ten Exam Scores

Take ten exam scores: 72, 85, 90, 68, 77, 88, 91, 74, 82, 79. The sum is 806, so the mean is 806 ÷ 10 = 80.6. Sorted, the list reads 68, 72, 74, 77, 79, 82, 85, 88, 90, 91. With an even count, the median is the average of the two middle values: (79 + 82) ÷ 2 = 80.5. Every value appears exactly once, so there is no mode. The range is 91 − 68 = 23. For standard deviation, square each distance from the mean (80.6), add them to get 564.4, and divide: by 10 for the population value, giving 7.51, or by 9 for the sample value, giving 7.92.

Read together, these numbers describe the class well. The mean and median nearly agree (80.6 and 80.5), which says the distribution is fairly symmetric — no extreme score is dragging either one away. The standard deviation of about 7.5 says a typical score sits roughly seven or eight marks from the mean, and the range of 23 says the gap between the weakest and strongest paper is substantial but not wild. If one student had scored 20 instead of 68, the mean would fall to 75.8 while the median would barely move — a live demonstration of why reporting both is the honest choice. For marks-to-percent work, see the percentage calculator.

Try the same dataset in the calculator above to see every figure reproduced: paste the ten scores, read the mean, median, range, and both standard deviations, then change one score and watch which measures move and which stay put. That experiment teaches more than any definition, because it shows the mean responding to every change while the median responds only when the middle of the list changes.

Two Classes, Same Mean, Different Story

The table below is the strongest argument for looking beyond the mean. Two classes both average 70, yet no teacher would call them equal. One is tightly bunched, the other spread from borderline failure to near perfection, and only the range and standard deviation reveal that.

Class A needs extension work for everyone at once, because the whole group sits together. Class B needs two different plans: support for the students at 50 and 60, and harder material for those at 80 and 90. A single average hides both needs. Whenever you compare two groups — two classes, two teams, two products — compare their spreads as well as their centres, or the comparison will mislead you.

Averages in Sport, Weather and Daily Life

Sport lives on averages. A batter who scores 300 runs in 10 innings averages 30, but that single number hides whether the runs came steadily or from one huge innings — which is why commentators also quote recent form and highest scores. Bowling averages work the other way round (runs conceded per wicket), so a lower bowling average is better, a reminder to always check which direction “good” points in before comparing.

Weather averages carry a different warning: the average rainfall for a month is a total divided by days, and it says nothing about whether the rain fell steadily or in one storm. Average speed is the subtlest of all. Drive 60 km at 60 km/h (one hour) and another 60 km at 30 km/h (two hours), and your average speed is 120 km ÷ 3 hours = 40 km/h — not the simple mean of the two speeds, 45 km/h. The trap is that the slower leg takes longer, so it deserves more weight. Whenever the things being averaged took different amounts of time, money, or effort, a plain mean is the wrong tool and a weighted average is the right one.

Mean, Median and Mode Explained in Depth

The three main averages answer three different questions. The mean asks what each value would be if the total were shared equally. The median asks what sits in the middle when the values are lined up in order. The mode asks what turns up most often. A good report often needs more than one of them, because each one hides something the others reveal. The calculator at the top of this page gives you all three at once, together with the range and standard deviation, so you can see the centre and the spread side by side.

The Arithmetic Mean, Step by Step

To find the arithmetic mean, add all the values and divide the total by how many values there are. For the numbers 4, 8, 9, 12, 12, 15 and 20, the sum is 80 and there are 7 values, so the mean is 80 divided by 7, which is 11.43 when rounded to two decimal places. Every value counts in this calculation, including the smallest and the largest, which is both the strength of the mean and its weakness. It uses all the information, but a single extreme value can pull it a long way from the rest of the data.

• It uses every value. Change any one number and the mean changes, even if the change is far from the middle of the list.
• It supports further arithmetic. Multiply the mean by the count and you recover the total, which is useful for budgets, totals and planning.
• It needs numbers. The mean has no meaning for pure categories such as favourite colours, where there is nothing to add up.
• It suits symmetric data. When values spread fairly evenly on both sides of the centre, the mean is a fair summary of the typical value.
• It is sensitive to outliers. One very large or very small value can move the mean well away from where most values sit.

The Median: The Middle Value

To find the median, sort the values from smallest to largest and take the middle one. With an odd count, the median is a value from the list itself. With an even count, it is the average of the two middle values, and it may be a number that never appears in the list. In the example above, the sorted list is 4, 8, 9, 12, 12, 15, 20, so the median is the fourth value, 12. The median is stubborn in a useful way: move the largest value from 20 to 200 and the median stays at 12, because the order of the middle values has not changed. That resistance is exactly why the median is the preferred headline for house prices, incomes and waiting times, where a few very large values would otherwise distort the picture.

The Mode: The Most Common Value

The mode is the value that appears most often. In the example above, 12 appears twice and every other value appears once, so the mode is 12. The mode is the only one of the three averages that works for categories as well as numbers: the modal shoe size, the most common survey answer and the most frequent exam mark are all modes. A dataset can have no mode, one mode or several modes. If two values tie for the highest frequency, both are modes and the data is described as bimodal. That tie is itself informative, because it can signal two distinct groups mixed together, such as beginners and experienced learners in the same class.

Notice how close the three averages are in this small example: 11.43, 12 and 12. When the mean, median and mode agree closely, the data is fairly balanced and any of the three gives a reasonable summary. When they disagree, the disagreement is the story. A mean well above the median points to large values pulling the average up, while a mean well below the median points to small values pulling it down. Always read the three together before deciding which one to quote.

Weighted Averages in Detail

A weighted average gives some values more influence than others. It is the right tool whenever the values were not earned, measured or bought on equal terms: exam parts with different marks, courses with different credit hours, products bought in different quantities and journeys made over different distances. The simple mean treats every value as equal, which is only fair when every value really does carry the same weight.

1. List each value with its weight. The weight can be a percentage, a number of marks, a number of credit hours or a quantity, as long as every weight uses the same kind of unit.
2. Multiply each value by its weight. This step gives heavier values a larger share of the total.
3. Add all the products together. This is the weighted total.
4. Add all the weights together. This is the total weight.
5. Divide the weighted total by the total weight. The result is the weighted mean.

Weighted Average Worked Example: Course Marks

A student has four course parts: homework marked 85 with a weight of 20 percent, quizzes marked 90 with a weight of 20 percent, a midterm marked 78 with a weight of 25 percent and a final exam marked 88 with a weight of 35 percent. The products are 17.00, 18.00, 19.50 and 30.80, which add to 85.30. Because the weights add to 100 percent, the weighted mean is 85.30. The simple mean of the four marks is 85.25, which looks almost the same here, but the closeness is a coincidence of these particular numbers. Change the final exam mark and the weighted mean moves much faster than the simple mean, because the final exam carries 35 percent of the total. For help turning marks into percentages, use the percentage calculator.

Weights do not have to add to 100. Suppose three pieces of work are weighted 4, 3 and 2, with marks of 92, 84 and 76. The products are 368, 252 and 152, which add to 772, and the total weight is 9, so the weighted mean is 772 divided by 9, which is 85.78. The simple mean is only 84.00, because it gives the lowest mark the same influence as the highest, even though the highest mark carries twice the weight. The lesson is general: whenever you see weights, percentages or credit hours attached to values, divide by the total weight, not by the count of values. Dividing by the count is the single most common weighted-average error.

Average Speed and Average Rate

Average speed is total distance divided by total time. That definition matters, because it is not the same as averaging the speeds themselves. Speeds can only be averaged directly when each speed applies for the same amount of time. When each speed applies over the same distance instead, the slower speed takes longer, so it occupies more of the total time and deserves more weight in the average. The same logic applies to any rate: total output divided by total input, total cost divided by total quantity and total distance divided by total time.

Why Averaging Speeds Directly Fails

The table above shows the trap clearly. The simple mean of 60 and 30 is 45, but the true average speed is 120 km divided by 3 hours, which is 40 km per hour. The slower leg took twice as long, so it pulls the true average below the midpoint of the two speeds. A second journey makes the same point with different numbers: 30 km at 60 km per hour takes half an hour, and 30 km at 40 km per hour takes three quarters of an hour, so the whole 60 km takes 1.25 hours and the average speed is 48 km per hour, not the simple mean of 50 km per hour. Rates behave the same way with money. Buy 10 items at 2 dollars each and 20 items at 3 dollars each, and the average cost is 80 dollars divided by 30 items, which is 2.67 dollars per item, not the simple mean of 2.50 dollars, because more items were bought at the higher price.

1. Work out the time for each leg. Divide each distance by its speed.
2. Add the distances. This is the total distance travelled.
3. Add the times. This is the total time taken.
4. Divide total distance by total time. The result is the average speed.
5. Check the answer. For equal distances, the average speed must sit closer to the slower speed than to the faster one, because the slower leg took longer.

Averages With Outliers

An outlier is a value far removed from the rest of the data. It may be a genuine extreme, such as a record-breaking performance, or it may be a mistake, such as a misplaced decimal point or a reading taken with the wrong unit. Either way, the mean will follow it, the median will largely ignore it and the range will stretch to include it. The first job when you spot an outlier is to check whether it is real. A house price of 10 million in a street of homes priced near 300,000 deserves a second look at the source before it is allowed to move any average.

The table shows the effect in full. Adding a single value of 200 lifts the mean from 50 to 75, a jump of 25, while the median moves only from 50 to 51. The range leaps from 10 to 155. If you reported only the mean, you would describe a group whose typical value is 75, when five of the six values are 55 or below. Reporting the median alongside the mean prevents that misreading, and reporting the range shows how far the outlier sits from the rest. Neither measure alone tells the whole story, but together they warn the reader that something unusual is present.

The Trimmed Mean: Removing the Extremes

A trimmed mean removes a fixed share of the smallest and largest values before averaging the rest. It is a compromise between the mean, which uses everything, and the median, which effectively ignores everything except the middle. Take the scores 58, 62, 65, 70, 74, 78, 82 and 95. The sum is 584 and the mean of all eight is 73.00. Remove the lowest score, 58, and the highest score, 95, and the remaining six scores add to 431, giving a trimmed mean of 71.83. The trimmed mean sits below the full mean here because the removed high score was further from the centre than the removed low score. Trimming must be decided by a rule fixed in advance, such as removing the top and bottom 10 percent, and it must be disclosed. Removing values because you dislike the answer they produce is not trimming, it is cherry-picking.

• Check for errors first. A value that looks impossible is more likely a typo than a discovery, so verify the source before deciding what to do with it.
• Report the median as well as the mean. When the two disagree sharply, the gap itself is evidence of skew or outliers.
• Show the data, not just the summary. The sorted list in the calculator above lets any reader see an outlier for themselves.
• Consider a trimmed mean for judged scores. Sports judging often drops the highest and lowest scores so that one generous or harsh judge cannot decide the result alone.
• Never delete an outlier silently. If a value is excluded, say so, say why, and say what the result would have been with it included.

Averages of Grades and Scores

Grade averages go wrong most often when the parts being averaged were not worth the same number of marks. Two tests worth the same total can be averaged safely, whether you average the raw marks or the percentages. Two tests worth different totals cannot: the larger test must count for more, because it contains more marks. The safe method is always the same. Go back to raw marks, add the marks earned, add the marks available, and convert to a percentage only once, at the end. The basic calculator is useful for checking the additions in that method by hand.

Averaging Percentages With Different Totals

Consider a quiz scored 8 out of 10, which is 80 percent, and an exam scored 135 out of 150, which is 90 percent. Averaging the two percentages directly gives 85 percent, which understates the result. The student earned 143 marks out of 160 available, which is 89.4 percent when rounded to one decimal place, because the exam, with fifteen times as many marks as the quiz, dominates the total. The direct average of percentages treats the 10-mark quiz as equal to the 150-mark exam, which it plainly is not. The error grows whenever the totals differ a lot and the percentages differ a lot, which is exactly when it matters most.

• Convert percentages back to raw marks first. Multiply each percentage by its total, or use the original marks if you have them.
• Add the marks earned and add the marks available separately. Never add percentages that come from different totals.
• Convert once, at the end. Divide total marks earned by total marks available and multiply by 100.
• Keep real zeros in and missing work out. A zero for work submitted and failed counts; a blank for work never set should not drag the average down.
• State the weighting. A grade average is only reproducible if the reader knows how much each part was worth.

Running Averages and Moving Averages

A running average, also called a cumulative average, is the average of everything so far. After each new value arrives, the average is recalculated over the full set to date. It is the natural way to track a season average in sport, a term average in school or a year-to-date average in business, because early values matter less and less as more data arrives, while the average itself settles down and becomes more stable. A running average answers the question: across everything up to now, what is the typical value?

The sales table shows the settling effect. After Monday the average is just Monday itself, 120. A strong Tuesday lifts it to 130, a quieter Wednesday leaves it unchanged at 130, and by Friday, with five days included, the average of 140 reflects the whole week rather than any single day. Each new day still moves the average, but by less and less as the count grows.

Moving Averages Smooth Out Ups and Downs

A moving average looks at a fixed window of recent values and slides that window forward one step at a time, dropping the oldest value as each new one arrives. A three-day moving average of daily temperatures 20, 22, 24, 19, 21, 23 and 25 gives 22.00, then 21.67, then 21.33, then 21.00 and then 23.00. The daily figures jump up and down by as much as 5 degrees, while the moving averages move gently between 21 and 23, revealing the underlying trend without the daily noise. A longer window smooths more but reacts more slowly; a shorter window reacts faster but smooths less. Choosing the window is a trade-off between stability and responsiveness, and the choice should match the question being asked.

• Weather and climate. Moving averages reveal warming or cooling trends that daily readings hide.
• Sales and website traffic. A seven-day moving average removes the weekly pattern of busy weekends and quiet weekdays.
• Sport form. A moving average over the last five matches shows current form better than a single match or a whole season.
• Health tracking. A moving average of daily steps or weight smooths out single unusual days, which is why it pairs well with tools such as the BMI calculator and the calorie calculator.
• Finance. Moving averages of prices are widely used to show trends, but they describe the past and do not predict the future on their own.

Common Mistakes When Averaging

Most averaging errors are not arithmetic slips. They are choices made before any calculation: the wrong average for the data, weights ignored, groups combined carelessly or missing values treated as zeros. Each mistake below produces a number that looks plausible and is wrong, which makes it more dangerous than an obvious error. Checking for these mistakes takes a minute and saves a misleading conclusion.

Averaging Averages Without Their Counts

Averages cannot be averaged directly unless every group is the same size. To combine group averages correctly, recover each group’s total by multiplying its average by its count, add the totals, add the counts and divide again. The table below shows a group of 10 people averaging 80 and a group of 30 people averaging 60. The naive average of the two averages is 70, but the true combined average is 65, because the larger group, with the lower average, carries three times the weight. Whenever someone quotes an average of averages without giving the group sizes, treat the result as unproven until the counts are known.

• Averaging averages. Always weight group averages by group size before combining them, as the table above shows.
• Ignoring weights. Marks, credit hours, quantities and times are weights. Leave them out and the average answers a different question from the one asked.
• Using the mean for skewed data. Incomes, house prices and waiting times need the median as the headline, with the mean reported alongside it.
• Treating missing values as zeros. A missing reading is not a reading of zero. It should be excluded and the exclusion should be stated.
• Treating real zeros as missing. A genuine zero, such as no sales on a closed day or no goals in a match, is real data and belongs in the average.
• Rounding too early. Round intermediate results and the final answer can drift. Keep full precision until the last step, as the calculator above does.
• Quoting an average without its spread. A mean without a range or standard deviation hides whether the values were bunched together or spread widely.

Real-Life Uses of Averages

Averages turn a pile of numbers into a single figure a person can act on, which is why they appear in almost every part of daily life. A shopkeeper uses the average daily takings to judge whether a week was good or bad. A teacher uses the class average to judge whether a test was too hard. A runner uses average pace to judge whether training is working. A household uses average monthly spending to set a budget. In each case the average is useful only when it matches the decision: a budget built on a mean dragged up by one expensive month will overstate normal spending, while a budget built on a median may understate the need to cover occasional large bills. The right response is often to look at both, and to keep the underlying figures close at hand.

• Health and fitness. Average weight, average daily steps and average calorie intake over a week describe habits better than any single day. The TDEE calculator estimates daily energy needs, and the water intake calculator estimates daily fluid needs, both of which are averages over typical days rather than exact figures for one day.
• Money and pay. Average monthly income, average spending by category and average hourly pay all help with planning. The salary calculator converts pay between periods so that averages from different pay cycles can be compared fairly.
• Housing and borrowing. Average monthly housing costs and average interest paid over a loan term help compare options that differ in length and rate. The mortgage calculator shows how monthly payments are built from the underlying totals.
• Sport. Batting averages, bowling averages, average points per game and average pace all summarise performance, but each sport defines its average differently, so the definition must be checked before averages from different sports or eras are compared.
• Weather. Average temperature and average rainfall describe a climate, but they hide extremes. A place with a mild average can still have dangerous hot days and freezing nights, so averages should sit beside maximum and minimum figures.
• Shopping. Average price per unit lets shoppers compare pack sizes fairly. Divide the total price by the quantity in each pack and compare the per-unit figures, not the pack prices, and remember to compare the same unit in every pack.

1. Look at the sorted list. Check for outliers, typos and gaps before choosing any average.
2. Check for skew. If a few large or small values dominate, lead with the median and report the mean alongside it.
3. Ask whether weights apply. If some values count for more than others, use a weighted mean.
4. Ask whether the data is categorical. If the question is what is most common, the mode is the answer and the mean is meaningless.
5. Report the spread as well as the centre. Give the range or standard deviation, and the count, so the reader can judge how much trust the average deserves.

Frequently Asked Questions

Should I include zero values in an average?

Yes, if the zero is real data. A student who missed a test and scored 0 has a result, and leaving it out inflates the average dishonestly. Only exclude a zero when it means “no measurement taken” — a missing reading, not a failed one. The distinction is about what the zero means, not about making the average look better.

Can I average percentages directly?

Only when every percentage shares the same base. Averaging 50% on a 10-mark quiz with 90% on a 100-mark exam gives 70%, but the true overall mark is (5 + 90) ÷ 110 = 86.4%. Percentages with different bases must be weighted by their bases first — convert back to raw marks, add those, then convert once at the end.

What is the difference between mean and average?

In everyday speech they are the same thing. In statistics, “average” is the umbrella term covering mean, median, and mode; “mean” specifically means sum divided by count.

When should I use the median instead of the mean?

When the data is skewed by outliers — incomes, house prices, waiting times. The median resists extremes; the mean does not.

What if there is no mode?

If every value appears exactly once, there is no most-common value, and the calculator says so. With ties, all tied values are listed.

Population vs sample standard deviation — which one?

Population (÷ n) describes the complete list you entered. Sample (÷ n − 1) estimates a larger population from your list. For a full dataset, use population.

How do weighted averages work?

Multiply each value by its weight, add the products, and divide by the total weight. Heavier weights pull the average toward their values.

Does the Average Have to Be One of the Numbers?

No. The mean of 4 and 5 is 4.5, which appears in neither value, and the median of 10, 20, 30 and 40 is 25, the average of the two middle values, which also appears nowhere in the list. Only the mode must be a value from the data, because it is defined as the most frequent value. This is why an average can be a fraction, a decimal or a value between two whole numbers even when every input is a whole number, and why rounding an average to a whole number can sometimes mislead. An average family size of 2.4 children does not mean any family has 2.4 children; it means the total number of children divided by the number of families is 2.4.

What Is the Geometric Mean?

The geometric mean is used for growth rates, ratios and percentages that multiply together, where the arithmetic mean would overstate the result. For two numbers, it is the square root of their product. Suppose an investment grows by 10 percent in one year and 20 percent in the next. The growth factors are 1.10 and 1.20, whose product is 1.32, and the square root of 1.32 is 1.1489, so the equivalent steady growth rate is 14.89 percent per year, slightly below the arithmetic mean of the two rates, 15 percent. The difference is small over two years but grows over longer periods, which is why the geometric mean is the standard choice for average growth rates and for averaging ratios. For ordinary lists of amounts, such as test scores or heights, the arithmetic mean remains the right choice, and the square root calculator can check the square root step in the two-number case.

How Do I Average Numbers With Different Units?

Convert them to a common unit first, then average. Averaging 60 kilometres per hour with 40 miles per hour without converting mixes two different units and produces a number in no unit at all. The same rule applies to weights in kilograms and pounds, distances in miles and kilometres and money in different currencies. Once every value is in the same unit, the ordinary mean, median or weighted mean can be used. If conversion is not possible because the values measure different things, such as a test score and a height, they should not be averaged at all. A single average only makes sense when every input measures the same kind of quantity on the same scale.

To finish, run your own numbers through the calculator at the top of this page. Paste a real list, read the mean, median and mode together, look at the sorted list for outliers and try changing one value to see which measures move. That short experiment, repeated with a few different lists, builds a stronger feel for averages than memorising definitions, and it is the quickest way to learn which average to trust for the data in front of you.

Disclaimer: This calculator is for general statistics and education. For formal analysis, verify methods against a statistics reference or professional advice.