There are three types of representative values that describe the characteristics of data.
- Mean: total of the data ÷ number of data values
- Median: the middle value when the data is arranged in ascending order (if there is an even number of values, the mean of the two middle values)
- Mode: the value that appears most often (in a frequency distribution, the class value with the greatest frequency)
📘 Example ①
For the data 5, 3, 8, 3, 6, 7, 3, find the mean, median, and mode.
Answer: Mean = (5+3+8+3+6+7+3)/7 = 35/7 = 5.
In order: 3, 3, 3, 5, 6, 7, 8. Median = 4th value = 5.
Mode = 3 (appears three times).
For the data 5, 3, 8, 3, 6, 7, 3, find the mean, median, and mode.
Answer: Mean = (5+3+8+3+6+7+3)/7 = 35/7 = 5.
In order: 3, 3, 3, 5, 6, 7, 8. Median = 4th value = 5.
Mode = 3 (appears three times).
💡 Key Point
- Median: odd number of values→middle value, even number of values→mean of the two middle values
- When there are outliers (extremely large or small values), the mean is easily affected
Practice Problems
- For the data 10, 14, 8, 12, 16, 10, 18, find the mean, median, and mode.
Answer and Explanation
- Answer: Mean=(10+14+8+12+16+10+18)/7=88/7≒12.6. In order: 8,10,10,12,14,16,18. Median=12 (4th value). Mode=10 (appears twice).