Skodel Ltd is a small brewery that is undergoing a major expansion after a takeover by a large European brewery chain. Skodel Ltd produces a range of beers and lagers, and is renowned for the quality of its beers, winning a number of prizes at trade fairs throughout the European Union. The new parent company are reviewing the quality control mechanisms being operated by Skodel Ltd and are concerned at the quantity of lager in its premium lager brand, which should contain a mean of 330 ml and a standard deviation of 15 ml. The bottling plant manager provided the parent company with quantity measurements from 100 bottles for analysis (Table 2.25).

(a) From the data set calculate the mean and median.

(b) Repeat the analysis to calculate the standard deviation, quartiles (Q₁, Q₂, and Q₃), quartile range, and SIQR.

(c) Describe the shape of the distribution. Do the results suggest that there is a great deal of variation in quantity within the bottle measurements? Compare the assumed bottle average and spread with the measured average and spread.

(d) What conclusions can you draw from these results?

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326 344 333 346 339 353 310 351 350 348 Table 2.25 326 344 333 346 339 353 310 351 350 348 326 344 333 346 339 353 310 351 350 348 326 344 333 346 339 353 310 351 350 348 326 344 333 346 339 353 310 351 350 348 326 344 333 346 339 353 310 351 350 348 326 344 333 346 339 353 310 351 350 348 326 344 333 346 339 353 310 351 350 348 326 344 333 346 339 353 310 351 350 348 326 344 333 346 339 353 310 351 350 348