Limited access

A brewery is preparing a very limited release of a special new beer. A collector is able to buy five bottles, each labeled with a small serial number. Based only on these five serial numbers, the collector wants to estimate the total number of bottles that were released.

One method (Method A) of estimating the total number of bottles is to add the maximum and minimum serial numbers from the sample of five bottles. Another method (Method B) of estimating the total number of bottles is to multiply the maximum serial number by 120%.

Assume there are actually 245 bottles produced, with serial numbers 001 through 245, although this fact is unknown to the collector.

What is the difference between the maximum possible estimates from Method A and Method B?

If the five bottles had serial numbers as close to the median serial number as possible, what would have been the difference between the estimates from Method A and Method B?

Difference in maximums

Difference in medians

1

48

96

121

192

241

246

294

486

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