Warm-up
Three quick questions from earlier lessons.
Discover
Two players both average 10 points a game. One scores 9, 10, 11; the other 0, 10, 20. Who is more consistent?
- The first player
- Both: the means are equal
Key idea
The MAD measures spread around the mean.
The mean is the sum ÷ the count (the balance point). The mean absolute deviation (MAD) is the average distance of the values from the mean: find each distance (always positive), then average them. A larger MAD means more variability.
Worked example
Data 2, 4, 6, 8.
Mean 5
Sum 20 ÷ 4.
3, 1, 1, 3
Distances.
MAD = 2
Average.
Your turn, guided
Your turn: the mean of 3, 7, 8.
18 ÷ 3.
Practice ★
- The mean of 4 numbers is 15. What is their sum?
- The mean of 7 numbers is 20. What is their sum?
- Two classes both have a mean test score of 61. Class A has a MAD of 3 points and class B a MAD of 7 points. Which statement is true?
- Class B's scores are more spread out
- Class A's scores are more spread out
- The scores are equally spread, because the means are equal
Watch out!
Practice ★★
- Find the mean absolute deviation (MAD) of the data 8, 13, 15, 20.
- Find the mean absolute deviation (MAD) of the data 10, 13, 15, 18.
- Boss problem. Four plants grew 5, 12, 14 and 21 cm.
Exit ticket
Three questions to check you have got it.
- Find the mean absolute deviation (MAD) of the data 8, 13, 15, 20.
- Find the mean absolute deviation (MAD) of the data 10, 13, 15, 18.
- Find the mean absolute deviation (MAD) of the data 1, 8, 12, 19.
Summary card
Mean absolute deviation
Average distance from the mean.
Watch out: distances, not signed differences.