Investigating Data — NSW Year 9 Core Maths
Mean, median, mode and range, histograms and stem-and-leaf plots, shape, comparing data sets, sampling and bias. Six subtopics and 120 practice questions with worked solutions, aligned to MA5-DAT-C-01 and MA4-DAT-C-02.
Investigating Data in NSW Year 9
Investigating Data is about summarising, displaying and questioning data. Year 9 Core students revise averages and the range, read histograms and stem-and-leaf plots, then describe the shape of a distribution, compare two data sets using centre and spread, classify variables, and judge whether a sample or survey question gives trustworthy results.
The six subtopics below cover measures of centre and spread, histograms and stem-and-leaf plots, the shape of a distribution, comparing data sets, sampling and types of data, and bias and questionnaires. Investigating Data is one of the 13 topics in NSW Year 9 Core Maths and belongs to the Statistics and Probability strand. The first two subtopics revise the Stage 4 outcome MA4‑DAT‑C‑02, shape and comparison are Stage 5 Core content under MA5‑DAT‑C‑01, and sampling and bias come from MA5‑DAT‑P‑01, which goes beyond the Core outcomes. Box plots, the interquartile range and bivariate data follow in Year 10.
Subtopics
Investigating Data: common questions
How do you find the median of a set of data?
Sort the scores, then take the middle one. With an even number of scores, average the two middle ones: for \(3, 7, 8, 10, 12, 15, 18, 20\), the median is \(\frac{10 + 12}{2} = 11\).
When is the median better than the mean?
If the data are skewed or contain an outlier. One house that sells for \(\$4\,200\,000\) in a street where the rest sell for about \(\$650\,000\) drags the mean far above a typical price, but the median is hardly affected.
What does positively skewed mean?
Most of the scores are bunched at the low end, with a long tail stretching towards the high values. The few high scores pull the mean above the median, as happens with weekly incomes.
What is the difference between a census and a sample?
A census collects data from every member of the population, while a sample collects it from only part of the population. A sample is used when a census would be too costly or slow, or would destroy what is being tested.
Which NESA outcomes cover Investigating Data in Year 9?
Measures of centre, range and data displays revise the Stage 4 outcome MA4‑DAT‑C‑02. Shape and comparing data sets are Stage 5 Core content under MA5‑DAT‑C‑01. Sampling and bias come from MA5‑DAT‑P‑01, which goes beyond the Core outcomes.