Unit S1: Statistics 1

The basic ideas of mathematical modelling as applied in probability and statistics.

Use mathematical modelling in probability and statistics to connect the rule to the data and decision in the question.

This matters because mathematical modelling in probability and statistics determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply mathematical modelling in probability and statistics to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Mathematical modelling in probability and statistics is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Histograms, stem and leaf Using histograms, stem and leaf diagrams and box plots to diagrams, box plots. compare distributions.; Back-to-back stem and leaf diagrams may be required.; Drawing of histograms, stem and leaf diagrams or box plots will not be the direct focus of examination questions.

Use histograms, stem and leaf to connect the rule to the data and decision in the question.

This matters because histograms, stem and leaf determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply histograms, stem and leaf to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Histograms, stem and leaf is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Measures of location – mean, Calculation of mean, mode and median, range and median, mode. interquartile range will not be the direct focus of examination questions.; Students will be expected to draw simple inferences and give interpretations to measures of location and dispersion.; Significance tests will not be expected.; Data may be discrete, continuous, grouped or ungrouped.; Understanding and use of coding.

Use measures of location – mean, to connect the rule to the data and decision in the question.

This matters because measures of location – mean, determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply measures of location – mean, to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Measures of location – mean, is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Measures of dispersion – variance, Simple interpolation may be required.; Interpretation of standard deviation, range and measures of location and dispersion. interpercentile ranges.

Use measures of dispersion – variance, to connect the rule to the data and decision in the question.

This matters because measures of dispersion – variance, determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply measures of dispersion – variance, to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Measures of dispersion – variance, is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Skewness.; Concepts of outliers.; Students may be asked to illustrate the location of outliers on a box plot.; Any rule to identify outliers will be specified in the question.

Use skewness to connect the rule to the data and decision in the question.

This matters because skewness determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply skewness to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Skewness is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Elementary probability.

Use elementary probability to connect the rule to the data and decision in the question.

This matters because elementary probability determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply elementary probability to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Elementary probability is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Sample space.; Exclusive and Understanding and use of complementary events.; Conditional P(A′) = 1 − P(A), probability.; P(A ∪ B) = P(A) + P(B) − P(A ∩ B), P(A ∩ B) = P(A) P(B | A).

Use sample space to connect the rule to the data and decision in the question.

This matters because sample space determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply sample space to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Sample space is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Independence of two events.; P(B | A) = P(B), P(A | B) = P(A), P(A ∩ B) = P(A) P(B).

Use independence of two events to connect the rule to the data and decision in the question.

This matters because independence of two events determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply independence of two events to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Independence of two events is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Sum and product laws.; Use of tree diagrams and Venn diagrams.; Sampling with and without replacement.

Use sum and product laws to connect the rule to the data and decision in the question.

This matters because sum and product laws determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply sum and product laws to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Sum and product laws is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Scatter diagrams.; Linear regression.; Calculation of the equation of a linear regression line using the method of least squares.; Students may be required to draw this regression line on a scatter diagram.

Use scatter diagrams to connect the rule to the data and decision in the question.

This matters because scatter diagrams determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply scatter diagrams to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Scatter diagrams is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Explanatory (independent) and Use to make predictions within the range of values of the response (dependent) variables. explanatory variable and the dangers of extrapolation.; Applications and interpretations.; Derivations will not be required.; Variables other than x and y may be used.; Linear change of variable may be required.

Use explanatory (independent) to connect the rule to the data and decision in the question.

This matters because explanatory (independent) determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply explanatory (independent) to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Explanatory (independent) is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The product moment correlation Derivations and tests of significance will not be required. coefficient, its use, interpretation and limitations.

Use product moment correlation to connect the rule to the data and decision in the question.

This matters because product moment correlation determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply product moment correlation to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Product moment correlation is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The concept of a discrete random variable.

Use concept of a discrete random variable to connect the rule to the data and decision in the question.

This matters because concept of a discrete random variable determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply concept of a discrete random variable to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: concept of a discrete random variable is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Use the probability function p(x) = P(X = x) and cumulative distribution function F(x0) = P(X ≤ x0) for a discrete random variable.

Use probability and cumulative distribution functions to connect the rule to the data and decision in the question.

This matters because probability and cumulative distribution functions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply probability and cumulative distribution functions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Probability and cumulative distribution functions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Mean and variance of a discrete Use of E(X), E(X 2) for calculating the variance of X. random variable.; Knowledge and use of E(aX + b) = aE(X) + b, Var(aX + b) = a2 Var(X).

Use mean and variance of a discrete to connect the rule to the data and decision in the question.

This matters because mean and variance of a discrete determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply mean and variance of a discrete to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Mean and variance of a discrete is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The discrete uniform distribution.; The mean and variance of this distribution.

Use discrete uniform distribution to connect the rule to the data and decision in the question.

This matters because discrete uniform distribution determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply discrete uniform distribution to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: discrete uniform distribution is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The Normal distribution including Knowledge of the shape and the symmetry of the the mean, variance and use of tables distribution is required.; Knowledge of the probability of the cumulative distribution density function is not required.; Derivation of the mean, function. variance and cumulative distribution function is not required.; Interpolation is not necessary.; Questions may involve the solution of simultaneous equations.

Use normal distribution to connect the rule to the data and decision in the question.

This matters because normal distribution determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply normal distribution to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Normal distribution is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.