A hands-on activity using the capture-recapture method to estimate the number of SmartiesTM candy pieces in a population and to study the variability in individual estimates compared to an estimate based on the mean of many estimates. The activity was described in B. Dudley, "A practical study of the capture/recapture method of estimating population size, Teaching Statistics, 5 (3) (1983), 66-70.
Summary: A hands-on activity to study the variability of the capture/recapture technique for estimating population sizes, demonstrated using a population of Smarties candy as an example.
Specifics: The capture/recapture technique is used to arrive at estimates of the size of population of mobile animals using the formula:
a/d = c/b, where
a = number marked and released into the population,
b = size of the second catch,
c = the number recaptured in the second catch,
d = the size of the population as a whole
The contents of a box of smarties are poured into a saucer and all the sweets of red colour were counted (=a). After that, all the sweets are poured into a paper bag and shaken thoroughly. With an egg cup, without looking at the bag, the second sample (=b) was scooped and the number of red ones recaptured were recorded (=c). This exercise was repeated ten times and the mean was calculated. Finally, the number of Smarties in the model population were counted and compared with the estimates derived from the sampling. Students learn about the variability of individual estimates, which is quite large (remember that the mean of the estimate here is actually infinite since an observation of zero tagged items results in an infite estimate).
(Resource photo illustration by Barbara Cohen, 2020; this summary compiled by Bibek Aryal)