GED Mathematical Reasoning
Mean, Median & Data Displays
These are three different ways of answering "what is typical here?" The mean is the everyday average. The median is the middle value once things are in order. They can be far apart, and knowing which one a question wants is usually the whole test item.
The words first
- mean
- add everything up, divide by how many — the ordinary average
- median
- put them in order, take the middle one
- mode
- the value that shows up most often
- range
- biggest minus smallest
- outlier
- one value far away from the rest, which drags the mean but barely moves the median
The method
MEAN
sum of all the values
mean = ————————————————————————
how many values
MEDIAN — order first, always
odd count: the single middle value
2, 5, 9, 11, 40 → median is 9
even count: average the middle two
4, 6, 8, 10 → (6 + 8) ÷ 2 = 7
WHY THEY DIFFER
salaries: 30k, 32k, 35k, 36k, 400k
mean = 106,600 (dragged up by one outlier)
median = 35,000 (what a typical person actually earns)
Worked all the way through
The problem
Find the median of 12, 7, 3, 9, 15, 6.
- Step 1 — Put them in order, smallest to largest.3, 6, 7, 9, 12, 15
- Step 2 — Count them.There are 6 values. Six is even, so there is no single middle.
- Step 3 — Find the two middle ones.With 6 values, the middle two are the 3rd and 4th: 7 and 9.
- Step 4 — Average those two.(7 + 9) ÷ 2 = 16 ÷ 2 = 8
On the board
12, 7, 3, 9, 15, 6
the problem
3, 6, 7, 9, 12, 15
put them IN ORDER first
3, 6, [7, 9], 12, 15
6 values, so two sit in the middle
(7 + 9) ÷ 2
average the middle two
16 ÷ 2 = 8
Answer
8
A second one, in a different form
Test scores: 70, 85, 90, 75. What is the mean?
70 + 85 + 90 + 75
add them all
320
320 ÷ 4
divide by how many
80
Answer
80
The usual mistake
Finding the median without sorting the list.
Check yourself
The mistake that costs the most points: finding the median without putting the list in order first. Order it every single time, even when it looks close enough.
Practice it
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