Single Variable and Bivariant Statistics — NSW Year 10 Advanced Maths
Shape, quartiles, box plots and standard deviation for one variable, then scatter plots and lines of best fit for two. Ten subtopics and 200 practice questions, aligned to NESA outcomes MA5-DAT-C-01 and MA5-DAT-C-02.
Single Variable and Bivariant Statistics in NSW Year 10 Advanced
This topic covers statistics for one variable and for two. For single-variable data, Year 10 Advanced students describe the shape of a distribution, find quartiles and the interquartile range, draw and compare box plots, and use the mean and standard deviation \(\sigma\). For bivariate data, they draw scatter plots, fit lines of best fit and use linear models to make predictions.
The ten subtopics below start with shapes of distributions, quartiles and the IQR, box plots and parallel box plots, then standard deviation, comparing means and standard deviations, and comparing data sets, and finish with scatter plots, lines of best fit and bivariate data. It is one of the 16 topics in NSW Year 10 Advanced Maths and sits within the Statistics and Probability strand (NESA outcomes MA5‑DAT‑C‑01 and MA5‑DAT‑C‑02). It leads on to data analysis and statistics in Year 11 and 12.
Subtopics
Single Variable and Bivariant Statistics: common questions
What does standard deviation tell you?
It measures how spread out the scores are around the mean. For the scores 3, 4, 6, 8 and 9 the mean is 6 and the population standard deviation is \(\sigma\approx2.3\). A smaller \(\sigma\) means more consistent data.
How do you find the interquartile range?
Order the scores, find the median, then find the middle of the lower half \((Q_1)\) and of the upper half \((Q_3)\). The IQR is \(Q_3-Q_1\). For 8, 9, 10, 10, 11, 12, 13, 14, 14, 15, 15, 15, 17, \(Q_1=10\), \(Q_3=15\) and the IQR is 5.
What is a positively skewed distribution?
It has most of the scores at the lower end and a long tail stretching to the right. The mean is usually pulled above the median, so the median is often the better measure of centre.
What is the difference between interpolation and extrapolation?
Interpolation predicts a value inside the range of the data, using the line of best fit. Extrapolation predicts outside that range and is less reliable, because the trend may not continue.
Which NESA outcomes cover this topic?
Single-variable statistics, including quartiles, box plots and standard deviation, is MA5‑DAT‑C‑01. Bivariate data, scatter plots and lines of best fit are MA5‑DAT‑C‑02. Both are Core outcomes in Stage 5 of the NSW Mathematics K–10 Syllabus (2022).