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

Sort the values and take the average of the two middle ones. For 3, 5, 8, 10 the middle values are 5 and 8, so the median is (5 + 8) ÷ 2 = 6.5.

Can a data set have more than one mode?

Yes. If two values tie for most frequent, the data is bimodal; with more it is multimodal. If every value appears exactly once, there is no mode.

Which is better, the mean or the median?

The mean uses every value, but extreme values pull it toward them. The median is resistant to outliers, so it is usually the better 'typical value' for skewed data such as incomes or house prices.

The largest value minus the smallest value. It is the simplest measure of spread, but a single outlier can make it misleading. The interquartile range is more robust.

Mean, Median, Mode & Range Calculator With Steps

Definitions

Mean (average): add all the values and divide by how many there are.
Median: the middle value once the data is sorted. For an even count, the average of the two middle values.
Mode: the value that appears most often. There can be none, one or several.
Range: largest value minus smallest value.

Worked example

Data: 3, 7, 7, 2, 9, 4, 7.

Mean: 3 + 7 + 7 + 2 + 9 + 4 + 7 = 39, and 39 ÷ 7 ≈ 5.571.
Median: sorted, the list is 2, 3, 4, 7, 7, 7, 9. The 4th of 7 values is 7.
Mode: 7 appears three times, more than any other value.
Range: 9 − 2 = 7.

Mean vs. median: which to report?

When the data is symmetric, the mean and median are close, and either is fine. When the data is skewed, they split apart: a few very high incomes raise the mean income far above what a typical person earns, while the median stays put. As a rule, report the median for skewed data and the mean for symmetric data. A histogram shows which you have.

Have grouped data (a frequency table) instead of raw numbers? Use the grouped data calculator.

Why the mean, median and mode can disagree

In right-skewed data (like incomes or wait times), the long tail pulls the mean above the median, and the median above the mode.

Take incomes (in $1,000s) for 10 people: 32, 35, 38, 41, 45, 48, 52, 58, 64 and 250. The mean is 66.3, but nine of the ten people earn less than that. The median, 46.5, is a far better description of a typical income here. One very high value is enough to pull the mean away from everyone else.

Which average should you use?

Your data	Best average	Why
Roughly symmetric numbers (heights, test scores)	Mean	Uses every value; close to the median anyway
Skewed numbers or outliers (incomes, house prices, wait times)	Median	Not pulled by extreme values
Categories (favorite color, shoe brand)	Mode	The only average that works for non-numbers
Discrete counts (children per family)	Median or mode	“2.3 children” isn’t a real family

Weighted mean

When values count unequally, multiply each by its weight, add, and divide by the total weight. A course with homework worth 20% (score 90), a midterm worth 30% (score 75) and a final worth 50% (score 82) gives (0.2 × 90 + 0.3 × 75 + 0.5 × 82) ÷ 1 = 81.5, not the simple average of 82.3.

Common mistakes to avoid

Finding the median without sorting. The median is the middle of the sorted list, not of the list as typed.
Forgetting to average the two middle values. With an even count, the median is the average of the two middle values.
Saying “no mode” when there are two. If two values tie for most frequent, both are modes (the data is bimodal).
Reporting only the mean for skewed data. Give the median too, or readers will picture the wrong typical value.

Mean, median and mode in Excel, Google Sheets, TI-84 and Python

Software	How
Excel	=AVERAGE(range), =MEDIAN(range), =MODE.SNGL(range); =MODE.MULT(range) lists every mode.
Google Sheets	=AVERAGE, =MEDIAN and =MODE (or MODE.MULT).
TI-84	STAT › CALC › 1-Var Stats gives x̄ (mean) and Med; there is no built-in mode.
Python	statistics.mean, statistics.median and statistics.multimode(data).

Mean, Median & Mode Calculator

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