Topic 4 of 7Pearson EdExcel

Statistics & Probability

Data analysis, averages, graphs, and probability

What You'll Learn

Mean = Σx/n; Median = middle value; Mode = most commonTree diagrams show successive event probabilitiesP(A and B) = P(A) x P(B) for independent eventsHistogram: frequency density = frequency / class width

Averages:

Mean = sum of values ÷ number of values
Median = middle value when data is ordered (or average of two middle values)
Mode = most frequent value
Range = largest − smallest

Frequency tables: Calculate mean using Σ(fx) / Σf where f = frequency, x = midpoint.

Cumulative frequency graphs: Plot cumulative frequency vs upper class boundary. Median at n/2, IQR = UQ − LQ (at ¾n and ¼n).

Histograms: Frequency density = frequency ÷ class width. Area of bar = frequency.

Probability:

P(event) = favourable outcomes / total outcomes
P(A and B) = P(A) × P(B) (independent events)
P(A or B) = P(A) + P(B) − P(A and B)
P(not A) = 1 − P(A)
Tree diagrams for successive events

Correlation: Scatter graphs show positive, negative, or no correlation. Line of best fit used for prediction.

Key Points to Remember

1Mean = Σx/n; Median = middle value; Mode = most common
2Tree diagrams show successive event probabilities
3P(A and B) = P(A) x P(B) for independent events
4Histogram: frequency density = frequency / class width

Pakistan Example

Cricket Statistics — Pakistan's Favourite Data Analysis

Babar Azam's batting average (mean runs per dismissal) is calculated like any statistical mean. A cricket statistician uses frequency tables of runs scored, plots cumulative frequency to find the median score (50th percentile), and uses scatter graphs to correlate batting average with team win rate. Probability appears too: if Babar has a 60% chance of scoring 50+ in any game, P(scoring 50+ in 3 straight games) = 0.6³ = 0.216 ≈ 21.6%.

Quick Revision Infographic

Mathematics — Quick Revision