3.2 Using the calculator statistics mode for a small data set

The data in Table 3.1 give the usage, in tonnes, of polythene by eight UK cosmetic companies (Gilchrist 2000).

Using your calculator's Statistics Mode, find the mean and standard deviation of these numbers.
Without using a calculator, find the median of the data.
Without using a calculator, find the IQR of the data.

TABLE 3.1: The amount of polythene (in tonnes) used by a sample of eight UK cosmetic companies
$\phantom{0}\phantom{0}\phantom{0}8.001$	$\phantom{0}\phantom{0}29.400$	$\phantom{0}266.532$	$4298.700$	$\phantom{0}\phantom{0}94.500$	$2547.300$	$\phantom{0}676.200$	$\phantom{0}\phantom{0}\phantom{0}0.000$

Most calculators have two buttons that compute the standard deviation: one if the data are a sample, and one if the data are a population. In practice, data are almost never a population.

If you are using your calculator correctly, you should get (before rounding) $\bar{x} = 990.0791$ and $s = 1588.514579$ . If you get $s = 1485.919327$ for the standard deviation, you are using your calculator incorrectly, so please ask for help. You are probably pressing the incorrect button to get the standard deviation.

References

Gilchrist R. Regression models for data with a non-zero probability of a zero response. Communications in Statistics-Theory and Methods. Taylor & Francis; 2000;29(9-10):1987–2003.