Sheet 7 of 10 · Maths
Data and averages
Mean, median, mode, range, charts and probability. 8 rules, each with a worked example.
Averages
Mean
Mean equals total ÷ how many values
Example4, 7, 8, 9, 12: total = 40, and 40 ÷ 5 = 8Median
The middle value once they are in order
- Even number of values: halfway between the middle two
Example2, 9, 4, 7, 5 → 2, 4, 5, 7, 9 → median 5 · 3, 5, 8, 10 → (5 + 8) ÷ 2 = 6.5Tip: Put the numbers in order first!
Mode and range
Mode = the most common value · Range = biggest − smallest
Example3, 6, 6, 8, 11: mode = 6, range = 11 − 3 = 8Tip: MOde = MOst.
Finding a missing value
Total equals mean × how many values
ExampleMean of 4 numbers is 7; three are 5, 8 and 6. Total = 7 × 4 = 28, so the missing one = 28 − 19 = 9
Charts
Bar charts and pictograms
Always read the key and the scale first
- Check what each gridline is worth: the scale may go up in 2s, 5s or 10s
ExampleKey: 1 circle = 4 children, so 3½ circles = 14 childrenPie charts
Angle equals fraction of the total × 360°
- Each person is worth 360° ÷ total (30 pupils: 360° ÷ 30 = 12° each)
Example5 of 30 pupils choose red: 5/30 = ⅙, and ⅙ × 360° = 60°Tip: Half = 180° · quarter = 90°
Probability
The probability scale
Probability goes from 0 (impossible) to 1 (certain)
- impossible · unlikely · even chance (½) · likely · certain
Working it out
Probability equals favourable outcomes ÷ total outcomes
- P(not happening) = 1 − P(happening)
Example3 red and 7 blue counters: P(red) = 3/10 = 0.3, P(not red) = 0.7
Want the full explanation?
The study guide goes through each rule step by step, with more examples.