National 5 Maths: Standard Deviation, Quartiles and Comparing Data Sets

Statistics questions on the National 5 Mathematics calculator paper usually follow the same pattern: calculate a standard deviation or an interquartile range, then compare two data sets in a sentence about the context. Marks are lost less often in the arithmetic than in the comparison, which must say which set is higher on average and which is more consistent. This material trains the statistical skills of the course: comparing data sets using a calculated interquartile range and standard deviation, and forming a linear model from a line of best fit.

The quiz has twelve questions. After a quick mean, four ask for a sample standard deviation to two decimal places, three from a list of data and one from the totals $\sum x$ and $\sum x^2$, using the two versions of the formula that appear on the formulae list; one wrong option in each comes from dividing by $n$ instead of $n-1$. Two questions find quartiles and the interquartile range, one for an odd and one for an even number of values. Two ask for the two valid comparisons of a pair of data sets, one described by means and standard deviations and one by medians and interquartile ranges. One checks what happens to the standard deviation when the same number is added to every value, and two find the equation of a line of best fit from two points on it, one of them with an estimate.

The flashcards give the mean, both standard deviation formulae, what standard deviation measures, how to find quartiles when the number of values is odd or even, the interquartile range, how to write a comparison, the gradient and intercept of a line of best fit, and the formula $y-b=m(x-a)$.

The printable written work has eight longer questions to answer by hand: standard deviation with a full table of deviations, standard deviation from totals, choosing between two runners, quartiles of two classes and a comparison, a line of best fit with a warning about estimating too far outside the data, what a standard deviation of zero means, the weather in two towns, and a car's value against its age in pounds, with the meaning of the gradient. Each asks you to show working and write the conclusion in context, as National 5 marking expects.

In the oral practice exam an examiner asks one question at a time, gives the data in words, asks you to phrase comparisons properly, and ends with brief feedback. The material suits S4 pupils preparing for National 5 and adds calculation practice to the category's existing statistics questions.

• Calculate a sample standard deviation from data or from the totals Σx and Σx²
• Find quartiles and the interquartile range for odd and even numbers of values
• Compare two data sets in context using an average and a measure of spread
• Explain what a standard deviation shows about a data set
• Find the equation of a line of best fit from two points and use it to estimate

Practice material written by Zestly, based on the National 5 Mathematics course specification (Qualifications Scotland, formerly SQA; version 3.0, May 2023), statistical skills: comparing data sets using the interquartile range and standard deviation, and forming a linear model from a given set of data.