Sampling & data presentation

Edexcel Stats 1-2

A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.

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Edexcel 9MA0 revision notes Edexcel 9MA0 past papers

The topic on one screen

A population is the complete group of interest; a sample is the part actually observed. Sampling is useful because a census can be slow, expensive or destructive, but the method must produce data that represent the population.
For a simple random sample, every member has an equal chance of selection. Stratified sampling preserves known group proportions; systematic sampling selects at a fixed interval after a random start. Quota sampling avoids needing a sampling frame but allows interviewer choice; opportunity sampling is quick but often biased.
Use the Edexcel large data set as data, not trivia: know its variables, units, locations, selected months and years, and explain when that restricted time window or a missing value makes an inference unreliable.
In a histogram, area represents frequency, so $\text{frequency density}=\dfrac{\text{frequency}}{\text{class width}}$ . Compare areas, not just bar heights, when class widths differ.
For grouped data use class midpoints. Then $\bar{x}=\dfrac{\sum fx}{\sum f}$ and $s=\sqrt{\dfrac{\sum fx^2}{\sum f}-\bar{x}^2}$ . Both are estimates because every value in a class is represented by its midpoint.
Choose summaries to match the data: median and IQR resist outliers, while mean and standard deviation use every value. Cumulative-frequency graphs and box plots support percentile estimates and contextual comparisons of location and spread.
An outlier rule such as values below $Q_1-1.5\operatorname{IQR}$ or above $Q_3+1.5\operatorname{IQR}$ identifies values for investigation. Check source errors, units and missing values; do not delete a record automatically just because it is unusual.
A regression line estimates one variable from another within the observed range. Interpret its gradient in context, distinguish interpolation from extrapolation, and never turn correlation into a claim of causation.

Where students actually lose marks

A sampling-method name without a contextual procedure often earns no method mark. State the sampling frame, how numbers are generated or selected, and how repeats are handled.

Edexcel 9MA0 Statistics mark-scheme convention

Large-data-set answers need a fact tied to the question. For example, selected months cannot support a whole-year estimate; simply writing 'the data are not representative' is too vague.

Edexcel 9MA0 large data set assessment convention

When comparing distributions, give one contextual comparison of location and one of spread. A list of medians and standard deviations is calculation, not interpretation.

Edexcel 9MA0 data-interpretation convention

Try it — exam-style

Medium

ORIGINAL

A sixth form has 240 students in Year 12, 180 in Year 13 and 120 in an access year. A stratified sample of 45 students is required. Calculate the number selected from each group and describe how a simple random sample could be taken within each group.

(4)

(Total for Question 1 is 4 marks)

Medium

ORIGINAL

The times

t

minutes for 30 tasks are grouped as follows:

0<t\leq10

(frequency 4),

10<t\leq20

(10),

20<t\leq30

(12),

30<t\leq50

(4). Estimate the mean and the standard deviation of the times, giving both to 3 significant figures.

(6)

(Total for Question 2 is 6 marks)

Medium

ORIGINAL

A histogram represents rainfall

r

mm. The class

2<r\leq5

has frequency density 4, and the class

10<r\leq20

has frequency 10. Find the frequency in the first class and the frequency density in the second. The quartiles are

Q_1=3.2

and

Q_3=8.0

. Determine whether

r=18

is an outlier under the

1.5\operatorname{IQR}

rule, and state what should happen next.

(5)

(Total for Question 3 is 5 marks)

Hard

ORIGINAL

For 30 selected days from May to October at a large-data-set weather station,

x

is daily mean temperature in

^\circ\text{C}

and

y

is daily mean wind speed in knots. The temperatures range from

7

17

. A regression line is

y=11.8-0.42x

. Interpret the gradient, estimate the wind speed at

18^\circ\text{C}

, comment on reliability, and explain why these days alone should not estimate an annual mean wind speed.

(5)

(Total for Question 4 is 5 marks)

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

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Drill it properly

CG50 statistics guide

One-variable statistics, regression and distribution calculations on the CG50.

Formulae to Memorise

The statistical formulae and notation that are not supplied in every question.

A-level maths flashcards

Sampling, large-data-set facts and interpretation sentence frames.

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