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Sampling and data: A Level Maths knowledge organiser

Everything to know about sampling and data on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Population and sample
The population is everything you want to know about; a sample is the part you collect data from.
Random sample
Every member of the population has an equal chance of being chosen.
Outlier
A value far from the rest, often defined as more than 1.5 × IQR beyond a quartile.
Coding
Changing data with y = (x − a)/b to make the numbers easier, then undoing it.

Key formulas

Formulas marked with a label are given in the exam (we only say so where our formula sheet confirms it). Learn the rest.

Mean\(\bar x=\frac{\sum x}n=\frac{\sum fx}{\sum f}\)
Standard deviationIn the formula booklet: Edexcel, OCR\(\sigma=\sqrt{\frac{S_{xx}}n}=\sqrt{\frac{\sum x^2}n-\bar x^2}\)
Outliers (common rule)\( \(\text{or}\) \(>Q_3+1.5(Q_3-Q_1)\)
Coding \(y=\frac{x-a}b\)\(\bar x=a+b\bar y,\) \(\sigma_x=|b|\,\sigma_y\)

Worked example

Data are coded with y = (x − 100)/5. The coded mean is 3.2 and the coded standard deviation is 1.4. Find the mean and standard deviation of x.

  1. x = 100 + 5y, so x̄ = 100 + 5 × 3.2
  2. Adding 100 does not change spread; multiplying by 5 does: σₓ = 5 × 1.4

Answer: Mean 116, standard deviation 7

Common mistakes

  • Premature rounding and truncating
  • Quota sampling called random
  • Stratified sample sizes not rounded sensibly
  • Census and sample advantages swapped

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

  • Distinguish between a population, a sample and a census, and discuss the advantages and disadvantages of sampling compared with collecting data on everyone.
  • Classify data as qualitative or quantitative and discrete or continuous, and become familiar with the variables and structure of the large data set.
  • Calculate the variance and standard deviation from raw data and from summary statistics such as Σx and Σx², and interpret them as measures of spread.
  • Draw cumulative frequency diagrams from grouped data and use them to estimate the median, quartiles, percentiles and the number of values above a given value.
  • Draw and interpret scatter diagrams, describe the type and strength of correlation, and explain why correlation does not show that one variable causes another.
  • Use and interpret the product moment correlation coefficient as a measure of linear correlation, and describe the strength and direction it shows.

The printable sheet

Sampling and data knowledge organiser for A Level Maths: one A4 page of key definitions, formulas, a worked example and common mistakes
Sampling and data knowledge organiser (A Level Maths), A4. Download the PDF.

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