Median vs Mode — Definition, Formula & Examples
Median vs mode compares two ways to describe the center of a data set. The median is the middle value when data is ordered from least to greatest, while the mode is the value that appears most often.
For an ordered data set of values, the median is the value at position if is odd, or the mean of the values at positions and if is even. The mode is the value with the greatest frequency; a data set may have no mode, one mode, or multiple modes.
How It Works
To find the median, arrange every value in order and pick the one in the middle. If there are two middle values, average them. To find the mode, count how many times each value appears and choose the one with the highest count. The median resists outliers because it only depends on position, not on how large or small extreme values are. The mode is the only measure of central tendency that works for non-numerical data, such as favorite colors.
Worked Example
Problem: Find the median and mode of this data set: 3, 7, 7, 9, 10, 12, 12, 12, 15.
Find the median: There are 9 values (odd count), so the median is the value in position (9 + 1) ÷ 2 = 5.
Find the mode: Count each value: 3 appears once, 7 appears twice, 9 once, 10 once, 12 appears three times, 15 once. The value 12 appears most often.
Compare: The median (10) and mode (12) differ. The median tells you the middle position; the mode tells you the most common value.
Answer: Median = 10, Mode = 12. They highlight different aspects of the same data set.
Visualization
Why It Matters
Choosing the right summary statistic matters in real decisions. A store manager uses the mode to stock the most popular shoe size, while a real-estate agent uses the median to report a typical home price without letting a few mansions skew the number.
Common Mistakes
Mistake: Forgetting to sort the data before finding the median.
Correction: Always arrange values from least to greatest first. Picking the middle entry from an unsorted list gives the wrong median.