Investigating Data — NSW Year 9 Advanced Maths
Summary statistics, data displays, the shape of a distribution, comparing datasets, sampling and bias. Six subtopics and 120 questions with worked solutions, aligned to NESA outcomes MA5-DAT-C-01 and MA5-DAT-P-01.
Investigating Data in NSW Year 9 Advanced
Investigating Data is about collecting, displaying and interpreting data to answer real questions. In Year 9 Advanced, students revise averages, the range and the main data displays, describe the shape of a distribution and its skewness, compare datasets by centre and spread, classify data and choose sampling methods, and spot bias in samples and survey questions.
The six subtopics below cover averages and the range, 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 14 topics in NSW Year 9 Advanced Maths and belongs to NESA's Statistics and Probability strand. It revises the Stage 4 outcomes MA4‑DAT‑C‑01 and MA4‑DAT‑C‑02 and covers the Stage 5 outcomes MA5‑DAT‑C‑01 and MA5‑DAT‑P‑01. It leads on to box plots and bivariate data later in Stage 5.
Subtopics
Investigating Data: common questions
When is the median better than the mean?
If the data is skewed or has outliers. Six house prices between $610,000 and $675,000 and one of $4,200,000 give a mean far above every typical house, but the median, $655,000, is a typical price.
What does positively skewed mean?
Most scores are at the low end and a tail stretches to the right, towards high values. The few large scores pull the mean above the median, as happens with weekly incomes.
How do you compare two datasets?
Compare a measure of centre, such as the mean or median, and a measure of spread, such as the range. The sets 18, 19, 20, 21, 22 and 5, 12, 20, 28, 35 have the same mean of 20 but very different ranges, 4 and 30.
What is the difference between a census and a sample?
A census collects data from every member of a population, while a sample uses part of it. A sample is needed when a census would cost too much or destroy the product, such as testing whether matches light.
Which NESA outcomes cover Investigating Data?
Averages, the range and data displays revise the Stage 4 outcomes MA4‑DAT‑C‑01 and MA4‑DAT‑C‑02. Shape and comparing datasets are the Stage 5 Core outcome MA5‑DAT‑C‑01, and sampling and bias are the Path outcome MA5‑DAT‑P‑01.