Measures of location and spread, diagrams for single and bivariate data, outliers and cleaning, correlation and the equation of a regression line, and interpolation versus extrapolation.

What this dot point is asking

Edexcel wants you to calculate and interpret measures of location (mean, median, mode) and spread (range, interquartile range, variance, standard deviation), draw and read histograms, box plots and cumulative frequency diagrams, identify and clean outliers, describe correlation, find and use the equation of a regression line, and know the difference between interpolation and extrapolation.

The answer

Location and spread

Outliers

Diagrams for data

Correlation and regression

Correlation describes the strength and direction of a linear relationship between two variables. A scatter diagram with points clustering tightly along a rising line shows strong positive correlation; points scattered around a falling line show negative correlation; a formless cloud shows little or none. The regression line of $y$ on $x$ has the form $y = a + bx$, where $b$ is the gradient (the change in $y$ per unit change in $x$) and $a$ is the intercept (the predicted $y$ when $x = 0$). It is used to predict $y$ from $x$.

Examples in context

Try this

Q1. For data with $\sum x = 50$, $\sum x^2 = 310$ and $n = 10$, find the mean and standard deviation. [3 marks]

• Cue. Mean $= 5$; variance $= \tfrac{310}{10} - 25 = 6$, so standard deviation $= \sqrt{6} \approx 2.45$.

Q2. A box plot has $Q_1 = 12$ and $Q_3 = 20$. Determine the outlier boundaries using $1.5 \times \text{IQR}$. [3 marks]

• Cue. IQR $= 8$; boundaries are $12 - 12 = 0$ and $20 + 12 = 32$.