The four averages: mean, median, mode and range
At Level 1 you need all four measures, not just the mode.
Mean = sum of all values ÷ number of values
Median = middle value when in order (or mean of two middle values)
Mode = most frequent value
Range = highest value − lowest value
Median = middle value when in order (or mean of two middle values)
Mode = most frequent value
Range = highest value − lowest value
💡 Median tip: Always sort the data first. For an even number of values, average the two middle ones: e.g. for 6 values, median = (3rd + 4th) ÷ 2.
Pie charts
A pie chart shows data as sectors (slices) of a circle. The full circle = 360°, representing 100% of the data. Each sector's angle is proportional to its share of the total.
Sector angle = (frequency ÷ total) × 360°
Frequency from angle = (angle ÷ 360) × total
Frequency from angle = (angle ÷ 360) × total
💡 Reading pie charts: Find the angle of the sector (with a protractor or given in the question), then use the formula to find the actual number or percentage.
Line graphs and trends
Line graphs show how data changes over time. Key skills are reading values at specific points, identifying trends (going up, going down, steady) and interpreting what the trend means.
Trend
Overall direction of the data
Interpolate
Read values between plotted points
Extrapolate
Estimate values beyond the data
Basic probability
Probability measures how likely an event is. It is always a number between 0 (impossible) and 1 (certain).
Probability = number of favourable outcomes ÷ total possible outcomes
Can be written as a fraction, decimal or percentage
Can be written as a fraction, decimal or percentage
0
Impossible
0.5
Even chance (50/50)
1
Certain
💡 Complementary events: P(event does NOT happen) = 1 − P(event happens). If P(rain) = 0.3, then P(no rain) = 0.7.
1Calculating all four averages
▼Test scores: 14, 18, 11, 18, 9, 15, 20. Find the mean, median, mode and range.
- 1Mean: (14+18+11+18+9+15+20) ÷ 7 = 105 ÷ 7 = 15
- 2Median: Sort: 9, 11, 14, 15, 18, 18, 20. Middle value (4th of 7) = 15
- 3Mode: 18 appears twice — all others once. Mode = 18
- 4Range: 20 − 9 = 11
✅ Mean=15 · Median=15 · Mode=18 · Range=11
2Finding median with even numbers
▼Hours of TV watched per week: 8, 12, 6, 15, 9, 11. Find the median.
- 1Sort the data: 6, 8, 9, 11, 12, 15
- 26 values — even number, so median = average of 3rd and 4th values.
- 33rd = 9, 4th = 11. Median = (9 + 11) ÷ 2 = 10
✅ Median = 10 hours
3Reading a pie chart
▼A pie chart shows 200 people's favourite sports. The "Football" sector has an angle of 126°. How many people chose football?
- 1Fraction of circle: 126 ÷ 360 = 0.35
- 2Number of people: 0.35 × 200 = 70
✅ 70 people chose football.
4Drawing a pie chart sector angle
▼30 students were asked their favourite subject. 12 chose Maths. What angle should the Maths sector be?
- 1Fraction: 12 ÷ 30 = 0.4
- 2Angle: 0.4 × 360 = 144°
✅ Maths sector = 144°
5Basic probability
▼A bag contains 4 red, 3 blue and 5 green counters. A counter is picked at random. What is the probability it is (a) blue, (b) not red?
- 1Total counters: 4 + 3 + 5 = 12
- 2P(blue) = 3 ÷ 12 = ¼ = 0.25
- 3P(red) = 4 ÷ 12 = ⅓. P(not red) = 1 − ⅓ = ⅔ ≈ 0.67
✅ P(blue) = ¼ | P(not red) = ⅔
6Mean from a frequency table
▼Find the mean number of goals scored per match from this frequency table:
| Goals | Frequency | Goals × Frequency |
|---|---|---|
| 0 | 5 | 0 |
| 1 | 8 | 8 |
| 2 | 6 | 12 |
| 3 | 3 | 9 |
| 4 | 2 | 8 |
| Total | 24 | 37 |
- 1Total goals: 0+8+12+9+8 = 37
- 2Total matches: 5+8+6+3+2 = 24
- 3Mean: 37 ÷ 24 ≈ 1.54 goals per match
✅ Mean ≈ 1.54 goals per match
Question 1
Data set: 3, 7, 4, 9, 7, 2, 8. What is the mean?
Question 2
Data: 5, 12, 7, 3, 12, 9, 8, 6. What is the median?
Question 3
A pie chart represents 120 students. A sector has an angle of 90°. How many students does it represent?
Question 4
A bag has 5 red, 4 blue and 1 yellow marble. What is the probability of picking a red marble?
Question 5
Scores: 6, 6, 8, 9, 11. What is the range?
Question 6
In a survey of 60 people, 15 chose "cycling". What angle should this sector be in a pie chart?
Question 7
P(winning a raffle prize) = 0.04. What is the probability of NOT winning?
Question 8
Ages in a group: 24, 31, 19, 28, 24, 35, 22. What is the mode?