The three representative values (mean, median, and mode) should each be used appropriately.
Points for Choosing
- Mean: represents the overall tendency when there are no outliers
- Median: used when there are outliers or when rank and order are important
- Mode: used when you want to know the value that occurs most often (such as clothing sizes and popular products)
📘 Example ①
Test results for a class (10 students): 50, 55, 60, 60, 65, 70, 70, 70, 75, 100.
Find the mean, median, and mode, and consider which representative value best represents this data.
Answer: Total=675. Mean=67.5. In order, median=(65+70)/2=67.5. Mode=70 (appears three times).
Because there is an outlier of 100 points, the median or mode is appropriate.
Test results for a class (10 students): 50, 55, 60, 60, 65, 70, 70, 70, 75, 100.
Find the mean, median, and mode, and consider which representative value best represents this data.
Answer: Total=675. Mean=67.5. In order, median=(65+70)/2=67.5. Mode=70 (appears three times).
Because there is an outlier of 100 points, the median or mode is appropriate.
💡 Key Point
- With outliers → median and mode are appropriate
- Without outliers → the mean is also effective
Practice Problems
- For the data 80, 85, 90, 85, 95, 100, 80, 85, find the mean, median, and mode.
Answer and Explanation
- Answer: Total=700. Mean=700/8=87.5. In order: 80,80,85,85,85,90,95,100. Median=(85+85)/2=85. Mode=85 (appears three times).