Single Variable and Bivariate Statistics — NSW Year 10 Core Maths
Shapes of distributions, quartiles and box plots, comparing data sets, scatter plots and bivariate data. Seven subtopics and 140 practice questions, each with a worked solution, aligned to NESA MA5-DAT-C-01 and MA5-DAT-C-02.
Single Variable and Bivariate Statistics in NSW Year 10 Core
Statistics in Year 10 Core covers two kinds of data. Single-variable data, such as test marks or travel times, is summarised with quartiles, the interquartile range, standard deviation and box plots, and compared across groups with parallel box plots. Bivariate data, such as height and arm span, is shown on scatter plots and modelled with a line of best fit to make predictions.
The seven subtopics below start with the shape of a distribution, move through quartiles, box plots and comparing data sets, and finish with scatter plots and bivariate data. Single Variable and Bivariate Statistics is one of the 11 topics in NSW Year 10 Maths Core and sits within NESA's Statistics and Probability strand (NESA outcomes MA5‑DAT‑C‑01 and MA5‑DAT‑C‑02). These skills lead into the data analysis of Stage 6 Standard and Advanced maths.
Subtopics
Single Variable and Bivariate Statistics: common questions
What is the interquartile range?
It is the difference between the upper and lower quartiles, \(Q_3 - Q_1\). It measures the spread of the middle half of the data, so unlike the range it is not thrown out by one very large or very small score.
How do you read a box plot?
The box covers the middle 50% of the scores, from the lower quartile to the upper quartile, and the line inside it is the median. The whiskers reach the lowest and highest scores, so each of the four sections holds about 25% of the data.
What does positively skewed mean?
A positively skewed distribution has most of its scores at the low end and a long tail to the right. The few large scores usually pull the mean above the median.
Which NESA outcomes cover Year 10 Core statistics?
Quartiles, box plots, standard deviation and comparing data sets come under MA5‑DAT‑C‑01. Scatter plots, lines of best fit and bivariate data come under MA5‑DAT‑C‑02. Both are Core outcomes of the NSW Mathematics K–10 Syllabus (2022).
Does a strong relationship on a scatter plot mean one thing causes the other?
No. Two variables can be associated without one causing the other. Ice-cream sales and shark sightings both rise in summer because of the hot weather, not because one leads to the other.