Topic 4 of 4Aga Khan Board

Statistics & Probability

Data handling, averages, graphs, and probability calculations

What You'll Learn

Mean = sum ÷ count; Median = middle; Mode = most frequentIQR = Q3 − Q1 (middle 50%)P(event) = favourable ÷ total outcomesMultiply probabilities for independent events

Measures of central tendency:

Mean = sum of all values ÷ number of values
Median = middle value when arranged in order
Mode = most frequently occurring value

Measures of spread:

Range = highest − lowest
Interquartile range (IQR) = Q3 − Q1 (middle 50% spread)

Graphs:

Pie charts — each sector represents a proportion (sector angle = value/total × 360°)
Bar charts — frequency on y-axis, categories on x-axis
Histograms — area of bar = frequency (used for grouped continuous data)
Frequency polygons — join midpoints of class intervals
Scatter graphs — show correlation (positive, negative, or none). Draw a line of best fit.

Probability:

P(event) = favourable outcomes ÷ total possible outcomes
P ranges from 0 (impossible) to 1 (certain)
P(A or B) = P(A) + P(B) for mutually exclusive events
P(A and B) = P(A) × P(B) for independent events
Tree diagrams help organise multi-stage probability problems.

Key Points to Remember

1Mean = sum ÷ count; Median = middle; Mode = most frequent
2IQR = Q3 − Q1 (middle 50%)
3P(event) = favourable ÷ total outcomes
4Multiply probabilities for independent events

Pakistan Example

Cricket Batting Averages — Statistics in Pakistan

Babar Azam's batting average is literally a statistical mean (total runs ÷ innings). When Pakistan selectors compare players using averages, medians, and consistency (low standard deviation), they are doing applied statistics. AKU-EB exam questions frequently use cricket, school survey data, or market prices as real-life statistical contexts.

Quick Revision Infographic

Mathematics — Quick Revision