Overview
This lesson explains the key concepts of Mean, Median, and Mode—three properties that summarize and simplify understanding of number data sets.
Understanding Data Sets
- A data set is a collection of numbers, often from measurements or surveys.
- Large data sets are hard to interpret without summary values.
Mean (Average)
- Mean and average are the same and describe the central value of a data set.
- To calculate the mean: add all the numbers, then divide by the number of values.
- Example: For numbers 1, 8, 3, 2, 6, the mean is (1+8+3+2+6)/5 = 20/5 = 4.
- Example: For ages totaling 222 and 6 family members, mean age is 222/6 = 37.
Median (Middle Value)
- Median is the middle value when the data set is arranged in order from least to greatest.
- If the number of items is odd, median is the center value.
- If the number of items is even, median is the mean of the two middle values.
- Example: For {1, 2, 3, 4}, median is (2+3)/2 = 2.5.
Mode (Most Frequent)
- Mode is the value that occurs most often in a data set.
- A data set may have no mode, one mode, or multiple modes if several values tie.
- Example: In {1, 2, 2, 3, 3, 3}, the mode is 3.
- Example: In {7, 7, 15, 15}, both 7 and 15 are modes.
Combined Example: Guitar Sales
- To find mean, add all monthly sales, then divide by 12 (total months).
- To find median, order the numbers and average the two middle months.
- To find mode, pick the sales figure that appears most frequently.
Key Terms & Definitions
- Data Set — a collection of numbers representing observed or measured values.
- Mean (Average) — sum of all values divided by the number of values.
- Median — the middle value in an ordered data set.
- Mode — the value that occurs most frequently in a data set.
Action Items / Next Steps
- Practice finding the mean, median, and mode on your own data sets.