Cogito
Grade 6 Math · Chapter 9 · Lesson 4
Mean, Median, and Which to Trust
One outlier can drag an average anywhere.
10 problems · about 19 minutes · 6.SP.A.3, 6.SP.B.5
What this lesson teaches
The child calculates mean and median and chooses which better summarises a data set.
- The mean shares the total equally between all the values.
- The median is the middle value once they are in order.
- One extreme value drags the mean but barely moves the median.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Dot Plots and Histograms: Bars of 2, 5 and 6. How many values in all?
Answer 13
Why 13.
Review — Centre and Spread: What is the mean of 6, 8, and 13?
Answer 9
Why 9.
Review — What Makes a Question Statistical: Is "How many siblings does each child in the club have?" statistical?
Answer Yes.
Why It anticipates variability.
Warm Up
Straightforward practice. Get the method working first.
3 problemsMedian of 2, 4, 6, 8 and 90?
Answer 6
Why 6.
Mean of 3, 5 and 7?
Answer 5
Why 15 ÷ 3.
Median of 1, 2, 3, 4 and 100?
Answer 3
Why The middle of five.
Build It Up
The same ideas with more to keep track of.
2 problemsMean of 1, 2, 3, 4 and 100?
Answer 22
Why 110 ÷ 5.
Which better describes 1, 2, 3, 4 and 100?
Answer The median.
Why The mean is above four of the five values.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Test Scores: Scores 4, 6, 8, 10 and 12. What is the mean?
Answer 8
Why 8.
The Middle: Scores 4, 6, 8, 10 and 12. What is the median?
Answer 8
Why 8 — with no outlier, the two agree.