Learning outcomes
- compute the median from ordered data
- identify the mode correctly
- distinguish median from mean
- handle odd and even numbers of observations
Median
- Median is the middle value of ordered data.
Odd number of observations
Example:2, 4, 6, 8, 10
6
Even number of observations
Example:2, 4, 6, 8
(4 + 6)/2 = 5
- Data must be arranged in order first.
Mode
- Mode is the most frequently occurring value.
1, 2, 2, 3, 4
2
Possible cases:
- one mode
- more than one mode
- no repeated value, so no mode in the simple sense
Mean vs median vs mode
- Mean: uses all values, sensitive to outliers
- Median: middle position, less affected by outliers
- Mode: most frequent value
Exam hints and traps
- Never find median from unordered data.
- With even number of observations, take the average of the two middle values.
- Mode is not always unique.
- Median is positional, mode is frequency-based.
Quick practice
- Find the median of
9, 3, 7, 5, 1. - Find the median of
2, 4, 6, 8, 10, 12. - Find the mode of
5, 5, 6, 7, 7, 7, 8.
Answer key
- Ordered data:
1, 3, 5, 7, 9; median =5 - Middle two values are
6and8; median =7 7