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ACMEM055

calculate and interpret statistical measures of spread, such as the range, interquartile range and standard deviation

ACMMM167

understand the effects of linear changes of scale and origin on the mean and the standard deviation.

ACMMM169

recognise features of the graph of the probability density function of the normal distribution with mean \(\mu\) and standard deviation \(\sigma\) and the use of the standard normal distribution

ACMGM030

determine the mean and standard deviation of a dataset and use these statistics as measures of location and spread of a data distribution, being aware of their limitations.

ACMMM141

recognise the variance and standard deviation of a discrete random variable as a measures of spread, and evaluate them in simple cases

ACMMM166

recognise the expected value, variance and standard deviation of a continuous random variable and evaluate them in simple cases

simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate the approximate standard normality of \(\frac{\overline X-\mu}{s/\sqrt[{}]n}\) for large samples \(\left(n\geq30\right)\), where \(s\) is the …

Overview of the senior secondary Australian Curriculum

ACARA has developed a senior secondary Australian Curriculum for English, Mathematics, Science and Humanities and Social Sciences. The senior secondary Australian Curriculum specifies content and achievement standards for each senior secondary subject. …

Overview of the senior secondary Australian Curriculum | Mathematics | Senior secondary curriculum

ACMGM019

calculate the volumes of standard three-dimensional objects such as spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations; for example, the volume of water contained in a swimming pool

ACMGM020

calculate the surface areas of standard three-dimensional objects such as spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations; for example, the surface area of a cylindrical food container.

ACMGM032

compare groups on a single numerical variable using medians, means, IQRs, ranges or standard deviations, as appropriate; interpret the differences observed in the context of the data; and report the findings in a systematic and concise manner

ACMMM174

understand the concept of the sample proportion \(\widehat p\) as a random variable whose value varies between samples, and the formulas for the mean \(p\) and standard deviation \(\sqrt[{}]{(p(1-p)/n}\) of the sample proportion \(\widehat p\)

ACMSM137

examine the concept of the sample mean X as a random variable whose value varies between samples where X is a random variable with mean μ and the standard deviation σ

ACMSM138

simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate properties of the distribution of \(\overline X\;\) across samples of a fixed size \(n\), including its mean \(\mu\), its standard deviation …

Links to Foundation to Year 10 Mathematical Methods

In Mathematical Methods, there is a strong emphasis on mutually reinforcing proficiencies in Understanding, Fluency, Problem solving and Reasoning. Students gain fluency in a variety of mathematical and statistical skills, including algebraic manipulations, …

Links to Foundation to Year 10 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM176

simulate repeated random sampling, for a variety of values of \(p\) and a range of sample sizes, to illustrate the distribution of \(\widehat p\) and the approximate standard normality of \(\frac{\widehat p\;-p}{\sqrt[{}]{(\widehat p(1-\widehat p)/n}}\) …

ACMMM178

use the approximate confidence interval \(\left(\widehat p-z\sqrt[{}]{(\widehat p(1-\widehat p)/n},\;\;\widehat p+z\sqrt[{}]{(\widehat p(1-\widehat p)/n}\right),\) as an interval estimate for \(p\), where \(z\) is the appropriate quantile for the standard …

ACMSM141

examine the approximate confidence interval \(\left(\overline{\mathrm X}\;–\frac{\mathrm z\mathrm s}{\sqrt[{}]n},\;\;\overline{\mathrm X}+\frac{\mathrm z\mathrm s}{\sqrt[{}]n}\right),\), as an interval estimate for \(\mu\) ,the population mean, where …

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