Investigating Data — NSW Year 8 Maths
Collecting, organising, graphing and summarising data, from samples to histograms and outliers. Nine subtopics and 180 practice questions with fully worked solutions, aligned to NESA outcomes MA4-DAT-C-01 and MA4-DAT-C-02.
Investigating Data in NSW Year 8
Statistics in Year 8 is about turning raw data into something you can read and trust. Students classify data, organise it in frequency tables, display it in sector graphs, dot plots, stem-and-leaf plots and histograms, and summarise it with the mean, the median, the mode and the range, then judge how an outlier or a skewed shape changes the picture.
The nine subtopics below start with organising and displaying data and the types of data, then cover the mean and mode, the median and range, frequency tables, dot plots and stem-and-leaf plots, and histograms and polygons, and finish with census and sampling and with choosing the best measure of centre. Investigating Data is one of the 14 topics in NSW Year 8 Maths and sits in the Statistics and Probability strand (NESA outcomes MA4‑DAT‑C‑01 and MA4‑DAT‑C‑02). In Stage 5 it leads on to quartiles, box plots and bivariate data.
Subtopics
Investigating Data: common questions
What is the difference between the mean, median and mode?
The mean is the total divided by the number of values, the median is the middle value once the data is in order, and the mode is the most common value. For 3, 4, 4, 6 and 13 the mean is \(30 \div 5 = 6\), and the median and mode are both 4.
How do you find the angle of a sector in a sector graph?
Divide the category’s frequency by the total and multiply by 360°. If 9 out of 40 students walk to school, the Walk sector is \(\frac{9}{40} \times 360^\circ = 81^\circ\).
What is an outlier and how does it affect the mean?
An outlier is a value far away from the rest of the data. It drags the mean towards it but barely moves the median, so the median is usually the better average for data with outliers, such as house prices.
Which NESA outcomes cover data in Year 8?
Data sits in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under two outcomes: MA4‑DAT‑C‑01 for classifying and displaying data, and MA4‑DAT‑C‑02 for analysing it with the mean, median, mode, range and shape.
What is the difference between a census and a sample?
A census collects data from every member of a population, like the national Census run by the Australian Bureau of Statistics. A sample uses only part of the population, which is quicker and cheaper, but it should be chosen at random to avoid bias.