Mathematics (AKU-MTH)
Topic 4 of 7Aga Khan Board

Statistics & Probability

Data handling, averages, graphs, and probability calculations

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.

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