Calcylator
Averages

Mean, median and mode:
pick the right average

Three different averages can tell three different stories about the same data. Learn how each one is found and which to quote.

Calcylator Editorial Team

Updated · 6 min read

Mean, median and mode defined

The mean is the sum of the values divided by how many there are, the median is the middle value once they are sorted, and the mode is the value that occurs most often. All three are called averages, but they answer slightly different questions.

The mean uses every number, so it reflects the total. The median only cares about position, so it ignores how extreme the ends are. The mode is the only one that works for categories such as the most common shoe size.

How to calculate the mean

Mean =mean = (x₁ + x₂ + … + xₙ) ÷ n
x₁ … xₙ:
the values in the list
n:
how many values there are
The calculator takes a list of numbers and returns mean(values), shown to four decimal places.

  • Monthly salaries (rupees)

    28,000; 30,000; 32,000; 32,000; 35,000; 38,000; 250,000

  • Sum

    445,000

  • Count

    7

Mean

63,571.43

445,000 ÷ 7 = 63,571.43 rupees.

  1. List all the values.
  2. Add them together.
  3. Count how many there are.
  4. Divide the sum by the count.

Finding the median and the mode

For the same seven salaries, sorted from lowest to highest, the median is the 4th value, 32,000. With an even number of values you average the two middle ones. The mode is 32,000 as well, because it appears twice and every other salary appears once.

Three averages of the same seven salaries
AverageHow foundResult (rupees)
Mean445,000 ÷ 763,571.43
Median4th of 7 sorted values32,000
Modemost frequent value32,000

With an even number of values the median is the average of the two middle ones. For 2, 4, 6, 8, 10 and 12 the middle pair is 6 and 8, so the median is 7, which here equals the mean of 42 ÷ 6 = 7. When data is evenly spread the two agree; when it is lopsided they drift apart.

The 250,000 salary pulls the mean to nearly double what most people earn. Without it, the mean of the other six is 32,500, close to the median.

Which average should you use?

  • Use the mean for roughly symmetric data without extreme values, such as repeated measurements of one length.
  • Use the median when a few very large or small values would distort the picture, as with salaries, house prices and delivery delays.
  • Use the mode for categories or counts, such as the most common size sold in a shop.
  • Quote more than one when they differ a lot, because the gap itself shows the data is skewed.

Think of a small firm with six staff on similar pay and an owner who takes a very large share of the profit. The mean wage across everyone looks generous, yet nobody on the shop floor earns it. Reporting the median, or both numbers together, avoids that false impression.

Many news headlines about average pay or property prices use the mean, which can overstate what a typical person gets. Asking for the median is a good habit.

Common mistakes with averages

  • Calling the mean the only average. Median and mode are equally valid.
  • Forgetting to sort before taking the median.
  • Averaging percentages or rates without thinking about weights; a mean of group means is not always the overall mean.
  • Ignoring that a dataset can have no mode, or several.

Common questions

What is the difference between mean, median and mode?

The mean is the sum divided by the count, the median is the middle value in sorted order, and the mode is the most frequent value. For 28,000 to 250,000 salaries the mean is 63,571.43 while the median and mode are 32,000.

How do you calculate the mean?

Add all the values and divide by how many there are. For 2, 4, 6, 8 and 10 the sum is 30 and the count is 5, so the mean is 6. The mean calculator does this for any list you enter.

When should I use the median instead of the mean?

Use the median when a few extreme values would distort the mean, such as salaries or house prices. One very large value can double the mean but leaves the median almost unchanged, giving a better picture of a typical case.

Can a dataset have more than one mode?

Yes. If two values appear equally often and more than any other, the data has two modes and is called bimodal. If every value appears once there is no mode, so you may report that no mode exists.

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