A-Level — mathsStandard1 min read

Sampling and Data Presentation

Understand sampling methods and data presentation at A-Level. Random, stratified, systematic, opportunity, and quota sampling.

Tutor AI Team
Tutor AI Team

A-Level Statistics requires understanding of sampling methods, their advantages and disadvantages, and data presentation techniques.

Sampling Methods

Method Description Pro Con
Simple random Each item has equal chance Bias-free Need sampling frame
Stratified Proportional from groups Representative Need population data
Systematic Every kkth item Easy, spread Can miss patterns
Opportunity Whoever's available Quick Biased
Quota Set numbers from groups No sampling frame needed Interviewer bias

Data Types

  • Quantitative: numerical (discrete or continuous).
  • Qualitative: categorical.

Measures of Central Tendency

Mean, median, mode. For grouped data: estimated mean using midpoints.

Measures of Spread

Range, IQR, variance, standard deviation.

σ2=∑(x−xˉ)2n=∑x2n−xˉ2\sigma^2 = \frac{\sum(x - \bar{x})^2}{n} = \frac{\sum x^2}{n} - \bar{x}^2

Coding

If y=x−aby = \frac{x - a}{b}, then xˉ=byˉ+a\bar{x} = b\bar{y} + a and σx=bσy\sigma_x = b\sigma_y.

Practice Problems

    1. When would you use stratified over simple random?
    1. Find the standard deviation of: 3, 5, 7, 9, 11.
    1. Data is coded: y=x−5010y = \frac{x - 50}{10}. yˉ=2.3\bar{y} = 2.3. Find xˉ\bar{x}.

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Key Takeaways

  • ✓

    Choose sampling method based on context.

  • ✓

    Standard deviation: σ=∑x2n−xˉ2\sigma = \sqrt{\frac{\sum x^2}{n} - \bar{x}^2}.

  • ✓

    Coding simplifies calculations.

Tags:
#a-level#maths#statistics#sampling#data

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