AQA Statistics 1

 

Numerical Measures

 

Standard deviation and variance calculated on ungrouped and grouped data.

 

 

 

 

 

Linear scaling

 

 

Choice of numerical measures

Candidates will be expected to be able to obtain standard deviation and mean values directly from calculators.  It is advisable for candidates to know whether to divide by n or (n – 1) when calculating the variance, but questions requiring this knowledge will not be set.

Artificial questions requiring linear scaling will not be set. But candidates should be aware of the effect of linear scaling on numerical measures.

Candidates will be expected to be able to choose numerical measures, including mean, median, mode, range and interquartile range, appropriate to given contexts.

Binomial Distribution

 

Discrete random variables

Only an understanding of the concepts;  not examined beyond binomial distributions

Conditions for application of a binomial distribution

Calculation of probabilities using formulae and tables.

 

 

The use of  notation.

Mean, variance and standard deviation of a binomial distribution.

Derivations will not be required.

Probability

 

Elementary probability; the concept of a random event and its probability.

Addition law of probability. 

Mutually exclusive events.

 

 

 

 

 

 

Multiplication law of probability and conditional probability.

 

Independent events.

 

Application of probability laws.

 

Assigning probabilities to events using relative frequencies or equally likely outcomes.  Candidates will be expected to understand set notation but its use will not be essential.

 

 two events only.

 two or more events.

.

 

; two or more events.

 

;  two or more events.

 

Only simple problems will be set that can be solved by counting equally likely outcomes and/or the use of tree diagrams or frequency tables.

Normal Distribution

 

Continuous random variables

Only an understanding of the concepts;  not examined beyond normal distributions.

Properties of normal distributions.

Shape, symmetry and area properties. Knowledge that approximately 2/3 of observations are within

m ± s and equivalent results.

Calculation of probabilities. 

Transformation to the standardised normal distribution and use of the supplied tables. Interpolation will not be essential; rounding z – values to two decimal places will be accepted.

Mean, variance and standard deviation.

To include finding unknown mean and/or standard deviation by making use of the table of percentage points.  (Candidates may be required to solve two simultaneous equations.)

Estimation

 

Population and sample

To include the terms ‘parameter’ and ‘statistic’.

Candidates will be expected to understand the concept of a simple random sample.  This will not be tested in the written examination.

Unbiased estimates of a population mean and variance.

 and  respectively.

The sampling distribution of the mean of a random sample from a normal distribution. 

To include the standard error of the sample mean,, and its estimator, .

A normal distribution as an approximation to the sampling distribution of the mean of a large sample from any distribution.

Knowledge and use of the Central Limit Theorem.

Confidence Intervals for the mean of a normal distribution with known variance. 

Only confidence intervals symmetrical about the mean will be required.

Confidence intervals for the mean of a distribution using a normal approximation. 

Large samples only. Known and unknown variance.

Inferences from confidence intervals

Based on whether a calculated confidence interval includes or does not include a ‘hypothesised’ mean value.

Extended (coursework-type) project to practice skills of this section

 

Correlation and Regression

 

Calculation and interpretation of the product moment correlation coefficient

 

 

 

 

Identification of response (dependent) and explanatory (independent) variables in regression.

 

Calculation of least squares regression lines with one explanatory variable.  Scatter diagrams and drawing a regression line thereon.

 

 

 

Calculation of residuals.

 

 

 

 

Linear scaling

Candidates should be encouraged to obtain correlation coefficient values direct from calculators.  Calculations from grouped data are excluded.  Importance of checking for approximate linear relationship but no hypothesis tests.  Understanding that association does not necessarily imply cause and effect.

 

 

 

 

 

Candidates should be encouraged to obtain gradient and intercept values directly from calculators.  Practical interpretation of values for the gradient and intercept.  Use of line for prediction within range of observed values of explanatory variable.  Appreciation of the dangers of extrapolation.

 

Use of (residual)i = yi – a - bxi. ..  Examination of residuals to check plausibility of model and to identify outliers.  Appreciation of the possible large influence of outliers on the fitted line. 

 

Artificial questions requiring linear scaling will not be set, but candidates should be aware of the effect of linear scaling in correlation and regression.