New Cur 21: Depression of the Mean

It is no surprise that the Statistics strand of the new mathematics curriculum is thin. Still, it may be a surprise how thin it is.

The following, as near as we can tell, is the complete list of contents and elaborations that refer to “mean” or “median” or similar, and thus might (and still might not) require at least some mental or written computation. In other words, these are the only items we could find that seem to not simply be a matter of tabulating or “exploring” or “investigating” or “analysing”, the only items that consist of anything more than sitting around and chatting about stuff.

Year 7

acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data (AC9M7ST01)

understanding that summarising data by calculating measures of centre can help make sense of the data, commenting on skewness or symmetry of data and the use of mean and median as representative measures (AC9M7ST01)

comparing the mean, median, mode and range of displays of data from a given context, and explaining how outliers may affect summary statistics (AC9M7ST01)

create different types of numerical data displays including stem-and-leaf plots using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode (AC9M7ST02)

comparing variation in attributes by category using split stem-and-leaf plots or dot plots; interpreting the shape of the distribution using qualitative terms to describe symmetry or skewness, “average” in terms of the mean, median and mode, and the amount of variation based on qualitative descriptions of the spread of the data (AC9M7ST02)

connecting features of the data display; for example, highest frequency, clusters, gaps, symmetry or skewness, to the mode, range and median, and the question in context; describing the shape of distributions using terms such as “positive skew”, “negative skew”, “symmetric” and “bi-modal” and discussing the location of the median and mean on these distributions (AC9M7ST02)

using mean and median to compare data sets, identifying possible outliers and explaining how these may affect the comparison; recognising how different displays make specific information about data more evident, including proportions, and measures of mean, mode or median, spread and extreme values; understanding that the median and the mean will be the same or similar for symmetric distributions but different for distributions that are skewed (AC9M7ST02)

comparing the mean and median of data with and without extremes; for example, estimation of standard measures for length or mass, informally considering for a given set of data what might constitute an unexpected, unusual or extreme data value (AC9M7ST02)

Year 8

using digital tools to simulate repeated sampling of the same population, such as heights or arm spans of students, recording and comparing means, median and range of data between samples (AC9M8ST03)

Year 9

analyse reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians (AC9M9ST01)

comparing data displays using mean, median and range to describe and interpret numerical data sets in terms of centre and spread using histograms, dot plots, or stem-and-leaf plots (AC9M9ST04)

Year 10

finding the five-number summary (minimum and maximum values, median, and upper and lower quartiles) and using its graphical representation, the box plot, as tools for both numerically and visually comparing the centre and spread of data sets (AC9M10ST02)

Optional (and closeted) Year 10

comparing the use of quantiles, percentiles, and cumulative frequency to analyse the distribution of data

comparing measures of spread for different data distributions, such as mean or median absolute deviations with standard deviations, and exploring the effect of outliers