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Statistics
Preserve statistical sampling, data presentation and interpretation, probability, statistical distributions and statistical hypothesis testing.
0
Objectives
10
Flashcards
10
Questions
90 min
Study time
AqaA LevelMathematicsPaper 3
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Syllabus checklist
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Statistical sampling1 objectives
- K1 Understand and use the terms population and sample; use samples to make informal inferences about the population; understand and use sampling techniques including simple random sampling and opportunity sampling; select or critique sampling techniques in context, including understanding that different samples can lead to different conclusions about the population.
Single-variable data diagrams1 objectives
- L1 Interpret diagrams for single-variable data, including understanding that area in a histogram represents frequency; connect to probability distributions.
Scatter diagrams and regression lines1 objectives
- L2 Interpret scatter diagrams and regression lines for bivariate data, including recognition of scatter diagrams with distinct sections of the population; understand informal interpretation of correlation; understand that correlation does not imply causation; calculations involving regression lines are excluded.
Central tendency and variation1 objectives
- L3 Interpret measures of central tendency and variation, extending to standard deviation; calculate standard deviation, including from summary statistics.
Outliers and data presentation1 objectives
- L4 Recognise and interpret possible outliers in data sets and statistical diagrams; select or critique data presentation techniques in context; clean data including dealing with missing data, errors and outliers.
Mutually exclusive and independent events1 objectives
- M1 Understand and use mutually exclusive and independent events when calculating probabilities; link to discrete and continuous distributions.
Conditional probability1 objectives
- M2 Understand and use conditional probability, including tree diagrams, Venn diagrams and two-way tables; understand and use the conditional probability formula P(A|B) = P(A intersection B) / P(B).
Probability modelling1 objectives
- M3 Model with probability, including critiquing assumptions made and the likely effect of more realistic assumptions.
Discrete and binomial distributions1 objectives
- N1 Understand and use simple discrete probability distributions, excluding calculation of mean and variance of discrete random variables; use the binomial distribution as a model and calculate probabilities using the binomial distribution.
Normal distribution1 objectives
- N2 Understand and use the Normal distribution as a model; find probabilities using the Normal distribution; link to histograms, mean, standard deviation, points of inflection and the binomial distribution.
Distribution selection1 objectives
- N3 Select an appropriate probability distribution for a context, with appropriate reasoning, including recognising when the binomial or Normal model may not be appropriate.
Hypothesis testing language1 objectives
- O1 Understand and apply the language of statistical hypothesis testing, developed through a binomial model, including null hypothesis, alternative hypothesis, significance level, test statistic, one-tail test, two-tail test, critical value, critical region, acceptance region and p-value; extend to correlation coefficients as measures of how close data points lie to a straight line and interpret a given correlation coefficient using a given p-value or critical value, excluding calculation of correlation coefficients.
Binomial hypothesis test for a proportion1 objectives
- O2 Conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret results in context; understand that a sample is used to make an inference about the population and that the significance level is the probability of incorrectly rejecting the null hypothesis.
Normal hypothesis test for a mean1 objectives
- O3 Conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context.
Use of data in statistics1 objectives
- 3.21 Use one or more real, sufficiently rich large data sets in advance of final assessment; use technology such as spreadsheets or specialist statistical packages to explore the data set; interpret real data in summary or graphical form; use data to investigate questions arising in real contexts; analyse subsets or features of the data using a calculator with standard statistical functions.
Key terms
populationfrequencyscatter diagramsstandard deviationoutliersmutually exclusiveconditional probabilityassumptionsbinomial distributionNormal distributionNormal modelnull hypothesis
Exam tips
- Statistical sampling exam tip 1: Write the method before the answer so the examiner can follow each step. Apply this to k1 Understand and use the terms population and sample; use samples to make informal inferences about the population; understand and use sampling techniques including simple random sampling and opportunity sampling; select or critique sampling techniques in context, including understanding that different samples can lead to different conclusions about the population..
- Single-variable data diagrams exam tip 1: Write the method before the answer so the examiner can follow each step. Apply this to l1 Interpret diagrams for single-variable data, including understanding that area in a histogram represents frequency; connect to probability distributions..
Common mistakes
- Statistical sampling common mistake 1: Show the method first, then give the final answer in the required form. Apply this directly to Statistical sampling.
- Single-variable data diagrams common mistake 1: Show the method first, then give the final answer in the required form. Apply this directly to Single-variable data diagrams.
Practice preview
- A test statistic is not in the critical region at the 5% significance level. State the conclusion.
- A test statistic is not in the critical region at the 5% significance level. State the conclusion.
- A test statistic is not in the critical region at the 5% significance level. State the conclusion.
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