Data & Statistics

Measures of Centre

Given a data set, e.g.: 3, 5, 7, 7, 9, 11, 14

• Mean: sum ÷ count = (3+5+7+7+9+11+14) ÷ 7 = 56 ÷ 7 = 8
• Median: middle value when ordered = 7 (the 4th value)
• Mode: most frequent value = 7
• Range: max − min = 14 − 3 = 11

Finding Median with Even Count

When there's an even number of values, the median is the average of the two middle values.

Example: 2, 4, 7, 9 → Median = (4 + 7) ÷ 2 = 5.5

Types of Graphs

• Bar chart: comparing categories
• Line graph: showing change over time
• Pie chart: showing parts of a whole (sectors sum to 360°)
• Stem-and-leaf plot: showing distribution while preserving data values
• Dot plot/Histogram: showing frequency distribution

Pie Charts

Each sector angle = (frequency ÷ total) × 360°

Example: If a sector represents 25% of data, its angle = 0.25 × 360° = 90°

Working Backwards & Key Tips

If the mean of 5 numbers is 12 and four of them sum to 52, the fifth number = (5 × 12) − 52 = 60 − 52 = 8

Key Tips

• Always order the data set first before finding median or range
• The mode can have multiple values or no mode at all
• Outliers (extreme values) affect the mean more than the median — the median is a better measure when outliers exist
• Read graph scales carefully, especially when they don't start at zero