WJEC Maths for AS: Applied sample

2 Data presentation and interpretation 32 (b) The regression equation for this dataset is: ‘Annual deaths’ = 23.95 – 1.03 × ‘Name length’ (i) Interpret the gradient of the regression equation for this model. [1] (ii) State with a reason, whether the regression model would be useful to predict the annual number of deaths for a new disease. [1] (iii) State whether the relationship between the ‘Annual deaths’ and ‘Name length’ is causal. Explain your answer. [1] Answer 2 (a) (i) Weak negative correlation. (ii) The fewer the number of letters in the name of the illness the higher the number of annual deaths. (b) (i) Each additional letter corresponds to a decrease in the number of deaths by 1030 on average. (ii) The model could not be used to predict annual deaths as the correlation is too weak. If you look at the annual deaths near zero, there is a very large difference in the corresponding name lengths. (iii) It is not causal, as the length of the name of an illness has no relation to how serious the illness is, nor to how many people are likely to suffer from it. 2.4 Measures of central tendency (i.e. mean, median and mode) A single value in a list of values that describes the centre of the data is called a measure of central tendency . There are three measures of central tendency: • Mean • Median • Mode Calculating the mean There are two types of mean: The population mean, μ and the sample mean, x . If the data used to calculate the mean is the entire population (e.g. every person in a company to work out the mean wage or every person in the school to work out the mean height), then the mean is called the population mean and it is given the symbol μ . If the population is too large to deal with, a representative sample can be taken that should represent the population and this sample is used to calculate the mean. When a sample is used the mean is called the sample mean and is given the symbol x .