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Statistics

Statistics

Mean, median, mode, variance and standard deviation, plus reading frequency tables and basic charts.

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Last reviewed Sep 2026 · GetCSCA editors

1. Statistics

Study order

Work the lessons top to bottom — each ends with practice, a timed set and a 5-stage drill. Then prove it in a full 48Q mock.

Statistics

Lesson 1 · target ~70s per question

Measures of center and spread (mean, median, mode, variance, σ) and interpreting tables and charts.

Why CSCA tests this

Statistics items test interpretation under outliers and units: picking mean vs median and reading variance as spread decides otherwise-trivial questions.

Key points — memorize

  • Match the center to the data: mean uses every value (efficient but outlier-sensitive), median uses order only (robust), mode uses frequency.
  • Order the data before any median: odd n takes the middle value, even n averages the two middle values.
  • Variance averages squared deviations and standard deviation σ is its root, restoring the original data units for interpretation.
  • σ = 0 exactly when all values are identical; otherwise larger σ means wider spread around the mean.
  • Read tables and charts literally first: confirm whether entries are counts or percentages and check axis labels and units before computing.

Formula sheet

  • mean x̄ = (Σx)/n
  • variance σ² = Σ(x − x̄)²/n
  • σ = √variance
  • Median position (odd n): (n+1)/2-th ordered value
  • Range = max − min
  • Median (even n): average of the two middle ordered values
  • Weighted/grouped mean: x̄ = (Σ fᵢxᵢ)/(Σ fᵢ)
  • σ = 0 ⇔ all values identical; larger σ ⇔ more spread (same units as data)

Classic traps

  • Taking the median of unordered data, or averaging all values for even n instead of the middle two.
  • Reporting variance units as data units (variance is squared units; σ carries the data units).
  • Using the mean on heavily skewed data with outliers where the median is the intended center.
  • Dividing by the wrong n in grouped means — total frequency Σfᵢ, not the number of groups.

Exam tactic

Sort the data on scrap paper as step zero — ordered values make median, range, and outlier-spotting automatic.

Worked examples

  1. Example 1: Find the mean and median of 2, 4, 4, 9.

    1. Mean: (2 + 4 + 4 + 9)/4 = 19/4 = 4.75.
    2. Ordered already; median = average of middle two: (4 + 4)/2 = 4.

    Answer: Mean 4.75; median 4

  2. Example 2: Data: 1, 2, 3. Find the population variance.

    1. Mean = 2; squared deviations: 1, 0, 1.
    2. Variance = (1 + 0 + 1)/3 = 2/3.

    Answer: 2/3

FoundationPractice →BasicPractice →CSCA StandardPractice →Timed set · ~70s/Q →

Previous exam questions

Real CSCA-style questions tagged to Statistics — answer right here.

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Related guides

1 lessons · one chapter

Finished Statistics? Prove it.

Run a timed set, clear every mistake, then take a full 48Q mock.

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