Median and mode
The median is the middle value when data is sorted. The mode is the value that appears most often. Both ignore how extreme the largest and smallest values are.
Last updated
Analogy
The median is the person standing in the middle of a queue sorted by height. The mode is the most popular flavour on the menu.
Example
Data: 3, 5, 7, 9, 100Median = 7 (middle of 5)Mean = 124 / 5 = 24.8Even count 2, 4, 6, 10:median = (4 + 6) / 2 = 5
In practice
Reports on income and house prices use the median because a few very large values would distort the mean.
Practice
Flashcards
- Which average resists extreme values: mean or median?The median. The mean is dragged toward extreme values.
Interview questions
- Data on household income has mean 52,000 and median 41,000. What does this tell you and which would you report?
- Mean above median suggests right skew
- A few high incomes pull the mean up
- Median is a better typical value
- Reporting both shows the gap
Questions people ask
How do you find the median when there is an even number of values?
Sort the data, then take the two middle values and find their mean. For 2, 4, 6 and 10 the middle pair is 4 and 6, so the median is 5. With an odd count, the median is simply the single middle value.
Can a data set have more than one mode?
Yes. If two values tie for the highest count, the data is bimodal, and with more ties it is multimodal. If every value appears once, there is no useful mode. The mode is also the only average that works for categorical data, such as the most common car colour.