A British statistician and biologist introduced a data set which consists of 50 samples from each of two species of Iris (Iris setosa and Iris versicolor). Four features were measured from each sample: the length and the width of the sepals and petals, in centimetres. This data set is available as Excel file "iris.xlsx" on Moodle in "Assessment" block.

1. a)Produce a histogram of the sepal length of Iris setosa and comment on the features of the distribution as shown by the histogram.
2. b)Determine the five-number summary for the sepal widths of Iris setosa.
3. c)Determine the five-number summary for the sepal widths of Iris versicolor.
4. d)Draw a comparative box-plot for the sepal widths of the two species, ensuring that any outliers are noted and that all axes are well labelled.
5. e)Comment on any similarities and differences (as shown in the comparative box-plot) in the sepal widths between the two species.
6. f)Find the mean and standard deviation of the sepal width for each type of Iris in the samples.
7. g)Compare the mean with the median for each type of Iris. What does each of these comparisons indicate about each distribution?

Combining groups can change the correlation coefficient, R-squared and overall trend between variables.

1. h)Draw a scatter plot and find the correlation coefficient and R-squared
2. for the sepal width and sepal length of Iris setosa,
3. for the sepal width and sepal length of Iris versicolor, and
4. for the sepal width and sepal length of the combined samples of Iris setosa and Iris versicolor.
5. i)State the effect of combining samples of Iris setosa and Iris versicolor on the correlation between the sepal width and sepal length.