Mean — Grade 7 Accelerated, what it means and where it is taught
Two kinds of centre: the balance point, and the middle value.
Taught in Grade 7 Accelerated.
Where it is taught
What uses it later
This idea is needed for:
- MAD — Mean absolute deviation — the average distance from the mean; a measure of spread.
- Standard deviation — A measure of typical distance from the mean.
- Normal distribution — The symmetric bell-shaped distribution described by its mean and standard deviation.
- z-score — How many standard deviations a value sits from the mean: z = x - μσ.
- Mean absolute deviation — The average distance of the values from the mean.
Practise this idea
47 questions in the course bank use Mean, in Positive & Negative Rational Number Operations, Sampling, Inferences & Comparing Populations, Scatter Plots & Association, Lines of Best Fit, Statistics: Centre, Spread & Displays, Quadrilaterals & Polygon Properties. The first 8 are below; the rest are in those units.
Problem 1
Compute (-3)2.
Worked answer
9
(-3)(-3) = 9
Same signs, positive.
Problem 2
Find the mean of 4, 8, 10, 14.
Worked answer
9
4 + 8 + 10 + 14 = 36
36 ÷ 4 = 9
Problem 3
The mean of 5 numbers is 12. What is their sum?
Worked answer
60
12 × 5 = 60
Problem 4
Find the mean absolute deviation of 4, 8, 10, 14.
Worked answer
3
Distances from 9: 5, 1, 1, 5
5 + 1 + 1 + 5 = 12
12 ÷ 4 = 3
Problem 5
A data set is 12, 15, 15, 18, 140. Which measure better describes a typical value?
- The mean
- The median
- They are equally good
Worked answer
The median
Mean = 2005 = 40
Median = 15
No value is near 40 — the outlier 140 dragged the mean away from the data.
Problem 6
Six numbers have a mean of 20. One of them, 35, is removed. What is the mean of the remaining five?
Worked answer
17
Total: 20 × 6 = 120
After removing: 120 - 35 = 85
85 ÷ 5 = 17
Problem 7
The mean of seven numbers is 15. Every number is increased by 4. What is the new mean?
Worked answer
19
The total rises by 7 × 4 = 28
New total: 105 + 28 = 133
133 ÷ 7 = 19 — shifting every value shifts the mean by the same amount.
Problem 8
Class A has mean 84 and MAD 2. Class B has mean 88 and MAD 3. How large is the mean gap relative to the MADs?
- Twice A's MAD and about 1.33 times B's MAD
- Half of each MAD
- Exactly equal to each MAD
Worked answer
Twice A's MAD and about 1.33 times B's MAD
The gap between means is 88-84=4.
Relative to A: 4/2=2 MADs. Relative to B: 4/3≈1.33 MADs.
This describes the separation; it is not a statistical significance test.