← Maths Standard 2 syllabus

NSWMaths Standard 2

Year 11: Data Analysis

10 dot points across 10 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How is a five-number summary turned into a box plot, and how do parallel box plots let you compare two groups by centre, spread, skew and outliers?

Construct and interpret box-and-whisker plots and use them, including parallel (side-by-side) box plots, to compare data sets in terms of centre, spread, skewness and outliers
A focused answer to the HSC Maths Standard 2 dot point on box-and-whisker plots. Building a box plot from the five-number summary, flagging an outlier with the 1.5 times IQR rule, drawing parallel box plots, and comparing two groups by centre, spread, skew and outliers, with worked Australian examples.
15 min answer →

How do you classify data as categorical or numerical, and how does the type of data decide which display is appropriate?

Classify data relating to a single random variable as categorical (nominal or ordinal) or numerical (discrete or continuous), and select and use an appropriate graphical display for the data type
A focused answer to the HSC Maths Standard 2 dot point on classifying data. Categorical (nominal versus ordinal) against numerical (discrete versus continuous), the questions that decide each branch, and choosing an appropriate display for each data type, with a classification tree and worked Australian examples.
13 min answer →

How are data collected and sampled so that the results fairly represent the whole population?

Investigate sampling techniques, including census, simple random, systematic and stratified sampling, and identify the target population and sources of bias in data collection
A focused answer to the HSC Maths Standard 2 dot point on data collection and sampling. Census versus sample, defining the target population, simple random, systematic and stratified sampling, choosing a sample size, designing a stratified sample with correct proportions, and spotting bias in a survey, with worked Australian examples.
14 min answer →

How are dot plots and stem-and-leaf plots used to display a data set and reveal its clusters, gaps, outliers and shape?

Display and interpret numerical data using dot plots and stem-and-leaf plots, including back-to-back stem-and-leaf plots, and describe the clusters, gaps, outliers and shape of the data
A focused answer to the HSC Maths Standard 2 dot point on dot plots and stem-and-leaf plots. How to construct and read each display, how to build a back-to-back stem-and-leaf plot to compare two groups, and how to describe clusters, gaps, outliers and the shape of a distribution, with worked Australian examples.
14 min answer →

How do you organise raw data into a frequency table, group it into class intervals with class centres, and build a cumulative frequency column?

Organise, interpret and display data into appropriate tabular and graphical representations including frequency distribution tables, both ungrouped and grouped using class intervals and class centres, and cumulative frequency
A focused answer to the HSC Maths Standard 2 dot point on frequency tables. Tallying raw data into a frequency table, grouping data into class intervals, finding the class centre, and building the cumulative frequency column, with worked Australian examples and the totals checked so the cumulative frequency ends at the sample size.
14 min answer →

How do you display grouped data as a frequency histogram and polygon, and read the median and quartiles off a cumulative frequency graph (ogive)?

Construct and interpret frequency histograms and polygons, and cumulative frequency graphs (ogives), including using an ogive to estimate the median and quartiles of a data set
A focused answer to the HSC Maths Standard 2 dot point on frequency graphs. Drawing a frequency histogram with a polygon overlaid through the bar-top midpoints, building a cumulative frequency graph (the ogive) from the running totals, and reading the median, the quartiles and the interquartile range off the ogive, with a fully worked grouped-marks example.
15 min answer →

How are the mean, median and mode used to summarise the centre of a data set, and which is the most appropriate measure?

Calculate measures of central tendency, including the mean, median and mode, for both raw data and data presented in a frequency table
A focused answer to the HSC Maths Standard 2 dot point on the mean, median and mode. Finding all three from a raw list, the mean and mode from a frequency table, the mean from grouped data using class centres, and choosing the most appropriate measure when the data is skewed or has an outlier, with worked Australian examples.
14 min answer →

How are measures of spread used to describe how widely data is spread out, and how do they let you compare two data sets?

Calculate measures of spread, including the range, quartiles and interquartile range, and the population standard deviation using technology
A focused answer to the HSC Maths Standard 2 dot point on measures of spread. The range, the quartiles and interquartile range, the five-number summary, the population standard deviation from a calculator, and how to compare the spread of two data sets, with worked Australian examples.
14 min answer →

How do you test whether a value is an outlier, name the shape of a data set, and write a full description of a distribution?

Determine outliers using the interquartile range, describe and interpret the shape and features of a distribution (symmetry, skewness, modality, centre, spread and outliers) and compare data displays using these features
A focused answer to the HSC Maths Standard 2 dot point on outliers and describing distributions. The 1.5 times IQR outlier test with lower and upper fences, telling symmetric from positively and negatively skewed data, unimodal versus bimodal shape, and writing a full describe-the-distribution answer covering shape, centre, spread and outliers, with worked Australian examples.
14 min answer →

Which statistical chart best displays a set of data, and how do you construct and read column, sector, line and Pareto charts correctly?

Display categorical and numerical data using a range of statistical graphs, including column graphs, sector graphs, line graphs, divided bar graphs and Pareto charts, and interpret the displays
A focused answer to the HSC Maths Standard 2 dot point on statistical graphs. Column and bar graphs, sector (pie) graphs with each angle computed as a fraction of 360 degrees, line graphs, divided bar graphs, and the Pareto chart with bars sorted descending and a cumulative percentage line for the 80/20 read, with worked Australian examples.
14 min answer →