Median — 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:
- Five-number summary — Minimum, Q1, median, Q3, maximum.
Practise this idea
19 questions in the course bank use Median, in Sampling, Inferences & Comparing Populations, Scatter Plots & Association, Statistics: Centre, Spread & Displays, Centre & Spread. The first 8 are below; the rest are in those units.
Problem 1
Find the median of 3, 7, 9, 12, 15.
Worked answer
9
Five values, so the middle is the 3rd
The median is 9.
Problem 2
Find the median of 4, 6, 9, 11.
Worked answer
7.5
Middle two are 6 and 9
6 + 92 = 7.5
Problem 3
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 4
On a plot of height against weight, one point is far above the pattern. It is
- an outlier
- a cluster
- the median
- impossible
Worked answer
an outlier
It does not follow the trend of the rest
So it is an outlier
Problem 5
Find the median of 3, 9, 4, 12, 7.
Worked answer
7
3, 4, 7, 9, 12
The middle value is 7
Problem 6
Find the median of 2, 5, 8, 11.
Worked answer
6.5
Middle two are 5 and 8
5 + 82 = 6.5
Problem 7
Find Q1 of 2, 4, 6, 8, 10, 12, 14, 16.
Worked answer
5
Lower half: 2, 4, 6, 8
4 + 62 = 5
Problem 8
Data: 20, 22, 24, 25, 400. Should you report the mean or the median?
Worked answer
median
400 is far from the rest
It drags the mean up to 98.2
The median, 24, is representative