Mean Median Mode Calculator

Use the mean median mode calculator to find all three averages of a data set at once. For 6, 3, 9, 4, 3, 8, 5, 3, 7, 12, the mean is the sum divided by the count, 60 ÷ 10 = 6. The median is the middle of the sorted list, (5 + 6) ÷ 2 = 5.5. The mode is 3, the value that appears most often.

How to use the mean, median and mode calculator

1. Choose List of numbers and type or paste your data. Commas, spaces, semicolons and new lines all work as separators.
2. If your data comes as a tally or frequency table (value and how many times it occurs), choose Frequency table and fill one row per value.
3. For grades, GPA or any average where some values count more than others, choose Weighted mean and enter each value with its weight.
4. Read the mean, median and mode at the top, then the count, sum, minimum, maximum and range. Pick how many decimal places you want with Round to.
5. Open Show steps for the full working, and try the outlier test to see why the median is often the better average.

Mean, median, mode and range formulas

In the formulas below, x stands for each data value, n is the number of values, and Σ (sigma) means “add them all up”.

Mean (the average)

Mean = Σx ÷ n. Add every value, then divide by how many values there are. The mean is what most people call “the average”. For 2, 3, 3, 5, 7, 10 the sum is 30 and n = 6, so the mean is 30 ÷ 6 = 5. The mean is often written x̄ (x-bar).

Median (the middle value)

Sort the values, then take the value in position (n + 1) ÷ 2. With an odd number of values that position is a whole number and the median is a single data value. With an even number of values the position ends in .5, so the median is the mean of the two middle values. For 2, 3, 3, 5, 7, 10 (n = 6), the middle values are the 3rd and 4th, 3 and 5, so the median is (3 + 5) ÷ 2 = 4.

Mode (the most frequent value)

The mode is the value that appears most often. In 2, 3, 3, 5, 7, 10 the mode is 3. A data set can have one mode, two modes (bimodal), more than two (multimodal) or no mode at all when every value appears the same number of times, as in 1, 1, 2, 2, 3, 3. When values tie, list every tied value; never average them.

Range, frequency tables and weighted means

Range = maximum − minimum, so the range of 2, 3, 3, 5, 7, 10 is 10 − 2 = 8. It measures spread, not center. For a frequency table, the mean is Σ(f × x) ÷ Σf, where f is the frequency of each value x. A weighted mean works the same way with weights w instead of frequencies: Σ(w × x) ÷ Σw. Our weighted average calculator covers that case in more depth.

Worked examples

Example 1: test scores (odd number of values)

Nine students scored 82, 90, 75, 90, 68, 85, 90, 77 and 85.

• Mean: the sum is 742 and n = 9, so the mean is 742 ÷ 9 ≈ 82.44.
• Median: sorted, the scores are 68, 75, 77, 82, 85, 85, 90, 90, 90. The middle position is (9 + 1) ÷ 2 = 5, and the 5th score is 85.
• Mode: 90 appears three times, more than any other score, so the mode is 90.
• Range: 90 − 68 = 22.

Example 2: a frequency table (even number of values)

A class survey asked 20 students how many pets they have: 4 have 0, 7 have 1, 5 have 2, 3 have 3 and 1 has 4.

• Mean: Σ(f × x) = 4 × 0 + 7 × 1 + 5 × 2 + 3 × 3 + 1 × 4 = 30, and Σf = 20, so the mean is 30 ÷ 20 = 1.5 pets.
• Median: n = 20 is even, so the median is the mean of the 10th and 11th values. The cumulative frequencies are 4, 11, 16, 19 and 20, so both the 10th and 11th values are in the row for 1. The median is 1.
• Mode: 1 has the highest frequency (7), so the mode is 1.

Example 3: one outlier (mean vs median)

Seven people earn 31, 35, 33, 36, 34, 32 and 250 thousand dollars a year. The mean is 451 ÷ 7 ≈ 64.43 thousand, yet six of the seven earn less than 37 thousand. The median, the 4th of the sorted values 31, 32, 33, 34, 35, 36, 250, is 34 thousand, which describes a typical person far better. There is no mode, because every value appears once. Without the 250, the mean would be 201 ÷ 6 = 33.5: a single extreme value nearly doubled the mean while the median barely moved.

Which average should you use?

A quick check: if the mean is much larger than the median, a few high values are pulling it up (the data is skewed right). If it is much smaller, a few low values are pulling it down (skewed left).

Mean, median and mode quick reference

Common mistakes

• Finding the median without sorting. The middle of the list as typed means nothing; sort first.
• Taking the wrong middle with an even count. With 10 values, the median is the mean of the 5th and 6th values, not the 5th value alone.
• Averaging tied modes. If 4 and 7 both appear most often, the modes are 4 and 7, not 5.5.
• Calling every value the mode. When all values appear equally often, the usual convention is that there is no mode.
• Ignoring frequencies. In a frequency table, dividing the sum of the values (0 + 1 + 2 + 3 + 4) by the number of rows gives 2 for the pets example, but the real mean is 1.5.
• Forgetting zeros and negatives. A 0 is a data value and must be counted in n, and negative values lower the sum.

Where mean, median and mode are used

Teachers report a class mean on a test, while news reports on income and home prices quote the median because a few very large values would distort the mean. Stores track the mode to know which size or product sells most. Your course grade is a weighted mean of homework, quizzes and exams. To go further, measure spread with the standard deviation calculator, or picture the median and quartiles with a box and whisker plot.

Mean, median and mode practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

Is the average the same as the mean?

Usually, yes. In everyday speech "average" means the arithmetic mean: the sum divided by the count. In statistics the median and mode are also called averages, or measures of center, so it helps to say which one you mean.

How do you find the median with an even number of values?

Sort the values and take the two in the middle, at positions n ÷ 2 and n ÷ 2 + 1. The median is their mean. For 10, 20, 30, 40 the middle values are 20 and 30, so the median is 25. The median need not be a data value.

Can a data set have more than one mode, or no mode?

Yes to both. If two values tie for the highest count the data is bimodal, and with more ties it is multimodal; list every tied value. If every value appears the same number of times, as in 1.5, 2.25, 3, 4.75, 6, there is no mode.

Can the mean, median and mode all be the same?

Yes. In a perfectly symmetric data set with one peak, such as 1, 2, 2, 3, 3, 3, 4, 4, 5, all three equal 3. When they differ, the gap between the mean and the median tells you which way the data is skewed.

Which is better, the mean or the median?

Use the mean when the data is roughly balanced and has no extreme values, because it uses every value. Use the median when there are outliers or the data is skewed, because one very large or very small value can move the mean a lot while the median stays put.

Related calculators

• Descriptive statistics calculator: quartiles, variance and more in one place
• Standard deviation calculator: how spread out the data is
• Weighted average calculator: grades and other weighted data
• Box and whisker plot maker: median, quartiles and outliers in a picture
• Stem and leaf plot maker: see every value and the mode at a glance