A sample of twelve sheep was randomly selected from a population and fed a special diet consisting of dried grass and barley for three months. At the end of the period the plasma insulin concentration ( U/ml)

20.5,26.2,18.8,21.2,22.1,21.2,25.4,26.8,22.9,22.8,30.8,28.420.5,26.2,18.8,21.2,22.1,21.2,25.4,26.8,22.9,22.8,30.8,28.4

a) Find the mean, median and mode.

b) Find the range, variance and standard deviation

c) Find the 40th percentile, 40P40.

d) Find the interquartile range (IQR). What does the IQR explain about the distribution of the plasma insulin concentration of the twelve sheep?

e) Identify the outliers if there are any. Justify your answer.

f) Sketch the box-and-whisker plot for the data set and comment on the shape of the distribution of the data.

g) Determine the proportion of plasma insulin concentrations falling within 2 standard deviations of the mean. Does the answer agree with the empirical rule?