Mean, Median, Mode Calculator

How to Use the Mean, Median, Mode Calculator

This mean median mode calculator finds the three main measures of central tendency for your dataset in one step. Enter your data values in the box and click Calculate. You can separate numbers with commas, spaces, tabs, semicolons or line breaks, so you can copy and paste a column straight from Excel or a text document.

Along with the mean, median and mode, the calculator shows the count, sum, minimum, maximum, range, variance, standard deviation and quartiles. The "Show working" section explains each result step by step, so you can check your homework or lab calculations.

You can also upload a CSV file. Choose the column you want to analyse and the tool fills in the numbers for you. Your file is read inside your browser and is never sent to a server.

What Are Mean, Median, and Mode?

Mean, median and mode are the three most common measures of central tendency. They describe the center, or typical value, of a dataset. Each one summarizes the data differently:

• The mean is the arithmetic average.
• The median is the middle value once the data are sorted.
• The mode is the value that occurs most often.

They don't always agree. Comparing all three tells you far more about your data than any one alone.

What Is the Mean?

The mean (also called the simple average or arithmetic mean) is the most widely used measure of central tendency. It is written µ for a population and x̄ ("x-bar") for a sample. The population mean uses every value in the group you care about. The sample mean uses only the observations you collected from it.

Steps to calculate the mean:

1. Add up all the values in the dataset.
2. Count the number of observations.
3. Divide the sum by the count.

Advantages and disadvantages of the mean. The mean is easy to understand and uses every value in the dataset. Its weakness is that outliers pull it up or down. Take 1, 2, 3, 4, 5, 6, 8 and 500. The sum is 529, so the mean is 66.125, which describes none of the eight values well.

What Is the Median?

The median is the middle value of an ordered dataset, the 50th percentile. Half the observations lie below it and half above. Each dataset has one median.

Steps to calculate the median:

1. Sort the values in ascending order.
2. Count the observations (n).
3. Pick the middle value if n is odd, or average the two middle values if n is even.

Advantages and disadvantages of the median. The median isn't skewed by extreme values, which makes it the better choice for skewed distributions such as household income. In 2, 3, 4, 5, 6, 7 and 1,000, the median is 5 while the mean is 146.7. The drawback is that the median ignores the size of most values. In 20, 50, 100, 120, 130, you could change 20 and 50 to any numbers below 100 and the median would stay at 100.

What Is the Mode?

The mode is the value that appears most often. It is the only one of the three that also works for categories, such as the most common soil type or the most frequent crop.

• Unimodal: one mode. In 1, 4, 9, 5, 5, 5, 9, 3 the mode is 5, which appears three times.
• Bimodal: two modes. In 2, 2, 3, 5, 5 the modes are 2 and 5.
• Multimodal: more than two modes.
• No mode: every value appears once, as in 1, 2, 3, 4, 5. Use the mean or median instead.

Steps to calculate the mode:

1. Sort the values.
2. Count how many times each value appears.
3. The value with the highest count is the mode.

For continuous data where no two values match exactly, group the data into intervals and report the modal interval, the interval with the highest frequency.

Worked Example: Mean, Median and Mode of 4, 6, 6, 8, 10, 10, 10, 12

You can enter the same numbers in the calculator above and compare.

Example for Agricultural and Research Data

Say a field trial records yields (t/ha) from seven plots: 3.2, 3.5, 3.5, 3.8, 4.1, 4.4 and 9.6.

The 9.6 plot, perhaps from a measurement error or an unusually good spot, pulls the mean well above the median. Without it, the mean is 3.75 t/ha. Reporting mean and median together shows readers that the data are skewed.

Comparison of Mean, Median, and Mode

Measure	Best used when	Affected by outliers?
Mean	Data are roughly symmetrical, no extreme values	Yes, strongly
Median	Data are skewed or contain outliers	No
Mode	Finding the most common value, or working with categories	No

When Are the Mean, Median, and Mode Equal?

The three are equal when a distribution is perfectly symmetrical and not skewed. In a right-skewed (positively skewed) distribution, the mean is larger than the median, because a few high values drag the mean upward. In a left-skewed (negatively skewed) distribution, the mean is smaller than the median. The bigger the gap between mean and median, the more skewed the data.

Which Measure of Central Tendency Is Best?

No single measure is best, and relying on only one is risky. Use the mean for symmetric data without outliers, the median for skewed data, and the mode for the most common value or for categories. Reporting all three, as this calculator does, gives the full picture of where your data are centered.

How to Calculate Mean, Median and Mode in Excel

You can check your results in Excel with these functions:

• Mean: =AVERAGE(A1:A10)
• Median: =MEDIAN(A1:A10)
• Mode: =MODE.SNGL(A1:A10), or =MODE.MULT(A1:A10) if there may be several modes

You can also copy the column from Excel and paste it into the calculator, or save the sheet as CSV and upload it.

Frequently Asked Questions