In an investigation of environmental causes of disease, data were collected on t

Question

In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, ppm) in the drinking water. Below, we provide some descriptive statistics for both variables, i.e. mortality and calcium concentration summary(calcium) Max Min. 1st Qu. Median Mean 3rd Qu 5.00 14.00 39.00 47.18 75.00 138.00 > summary(mortality) Min. 1st Qu. MedianMean 3rd Qu 1096 Max 1987 1379 1555 1524 1668 Here are histograms for both variables. Histogram of calcium 20 40 60 80 100 120 140 calcium

Explanation / Answer

a)

Mean and Median are measures of central tendency

We have the range as the measures of dispersion

Shapes- Calcium: Skewed to the right

Mortality: Can be approximated to be normal

Range for Calcium histogram = Max- Min = 138-5 = 133

Range for Mortality histogram = Max- Min = 1987-1096 = 891

For calcium, Mean = 47.18 ; Median= 39

For Mortality, Mean = 1524 ; Median= 1555

b)

Yes, as per the box-plots, outliers are those values which fall outside of Q1 and A3

So, for Calcium, outliers are all those values outside (14 , 75)

So, for Mortality, outliers are all those values outside (1379, 1668)

c)

i) It will be North with a value close to 1800

ii) It will be south with a value close to 1200

iii) It will be North with the mean around 1600

iv) It is more dispersed in South with a range value close to 700

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