The mean averages every value; the median is the middle value once they are in order.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Outliers change the choice
The median resists extreme values; the mean does not. Skewed data is better summarised by the median.
Spread
The range is maximum minus minimum. The interquartile range covers the middle half and ignores the extremes.
Pair them properly
Report the mean with the standard deviation, or the median with the IQR. Mixing a resistant measure with a non-resistant one is inconsistent.
Shape first
Look at the distribution before choosing. The shape decides which summary tells the truth.
Report both parts
A centre without a spread is half an answer. Two data sets can share a mean and look nothing alike.
Shape, centre, spread, outliers
A complete summary names all four in context. Reporting a mean alone conceals exactly the variability that made the question statistical in the first place.
Which measures suit which shape
Mean and standard deviation for roughly symmetric data; median and interquartile range when the data are skewed or contain outliers. The second pair is resistant, which is why it fits those cases.
Skew pulls the mean
In right-skewed data the mean exceeds the median. Comparing the two gives a numerical test for skew that needs no graph, and it explains why incomes are reported as medians.
Outliers are investigated
A flagged point may be an error or a genuine extreme value, and the two call for different responses. Removing one because it is inconvenient is not a statistical decision.
Step 2: Try It Yourself
Tap and try it out.
- Minimum4
- Lower quartile6
- Median9
- Upper quartile14
- Maximum18
- Interquartile range8
Each of the four sections holds a quarter of the values, however wide it looks. A narrow box means the middle half of the data is packed close together.
Step 3: Watch an Example
One step at a time.
Watch Kofi Choose a Summary
House prices in a street: 200, 210, 220, 230 and 900 thousand.
- Step 1
The total is 1760, so the mean is 352 thousand.
Step 4: Your Turn
Practice makes it stick.
The Mean
Problem 1 of 2
Data 4, 8, 12, 16. What is the mean?
The Median
Problem 2 of 2
Data 200, 210, 220, 230, 900. What is the median?
Summarise It
1 of 8
Data 3, 5, 7. Mean?
2 of 8
Data 2, 4, 6, 8, 20. Median?
3 of 8
Data 5, 9, 14, 20. Range?
4 of 8
Q1 = 6, Q3 = 15. IQR?
5 of 8
Which centre resists outliers? 1 mean, 2 median.
6 of 8
Which spread ignores the extremes? 1 range, 2 IQR.
7 of 8
Sort each measure by which summary it belongs with.
Tap something to move it.
- Empty
- Empty
8 of 8
Data 10, 20, 30, 40, 50. Mean?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Data 6, 10, 14. What is the mean?
Question 2 of 2
Which pairing is consistent?
What You Learned
- The mean averages; the median takes the middle and resists outliers.
- Range uses the extremes; the IQR uses the middle half.
- Report a centre and a spread that are consistent with each other.