Warm-up
Three quick questions from earlier lessons.
Discover
Five friends earn 10, 12, 13, 15 and 150 dollars an hour. Which number describes a typical friend better?
- The median, 13 dollars
- The mean, 40 dollars
Key idea
Two ways to measure the center.
Mean : the balance point; sensitive to extremes. Median: the middle value of the ordered data (with an even count, the average of the two middle values); resistant to extremes.
Worked example
Data: 4, 7, 7, 9, 13, 20.
Mean
Sum 60, six values.
Median
Middle values 7 and 9.
Mean > median: slight right skew
The 20 pulls the mean up.
Your turn, guided
Your turn: the median of 3, 8, 10, 15.
(8 + 10)/2.
Practice ★
- Find the mean of the data 5, 11, 24, 33, 41.
- Find the mean of the data 3, 11, 20, 38, 65.
- Find the mean of the data 9, 19, 24, 39, 68.
Watch out!
Practice ★★
- Find the median of the data 9, 14, 24, 37, 44, 79.
- Find the median of the data 2, 10, 28, 36, 43, 64.
- One value in a data set is changed from 20 to 712. What happens to the mean and the median?
- The mean increases; the median stays about the same
- Both increase by the same amount
- The median increases; the mean stays the same
Exit ticket
Three questions to check you have got it.
- Find the median of the data 9, 14, 24, 37, 44, 79.
- Find the median of the data 2, 10, 28, 36, 43, 64.
- Find the median of the data 8, 18, 26, 32, 43, 97.
Summary card
Center
- Mean: sum ÷ n; pulled by extremes.
- Median: middle value; resistant.
Watch out: even count: average the two middle values.