Fish Tag Lab
(Simulating to find an estimate of a Population)
We cannot tell the exact population of a species of fish in the lake. But we can take samples
to estimate the population by tagging the fish. In this lab you will use a sample to estimate
the population. We will be using beans! The beans will represent the population of fish in the
lake and you will need to estimate the number of fish (beans) in the lake (bag). You will be
given a bag of beans (fish) and you are not to count them!
Directions:
1. Take a marker and mark 25 of the beans from the bag and then return them to the
bag – you just marked your fish!
2. Thoroughly mix the beans.
3. Take a sample of 10 beans (with replacement and shake well between each draw) and
note the number of marked beans obtained.
4. Find the proportion of marked beans from your sample and record it as trial 1.
5. Repeat steps 2-4 twenty times for a total of 20 trials.
Trial #
1
2
3
4
5
6
7
8
9
10
#
Tagged
# not
Tagged
% Tag
Trial #
11
12
13
14
15
16
17
18
19
20
#
Tagged
# not
Tagged
% Tag
6. Find the mean (average) of the twenty sample proportions. This will represent the
proportion of tagged fish in the lake.
Mean = __________
7. Use this proportion and find the estimate of the total number of fish in the lake.
Work:
Total Number = ____________
8. Now mark 25 more of the beans for a total of 50 marked beans and return then to the
bag and repeat steps 2 – 7.
Trial #
1
2
3
4
5
6
7
8
9
10
#
Tagged
# not
Tagged
% Tag
Trial #
11
12
13
14
15
16
17
18
19
20
#
Tagged
# not
Tagged
% Tag
Mean = _____________
Work:
Total Number = _____________
9. Compare the estimate that you found in step 7 with 25 marked beans and the one you
found in step 7 with 50 marked beans. Do you think this is a good method for
estimating the population? Why or Why not? If not, how can we make it better?
10. Now find the true population percentage of tagged fish. How close were you?
This was adapted from an activity in Long, C & DeTemple, D. (2006). Mathematical Reasoning for Elementary Teachers, 4th edition.
Boston: Pearson found on page 524.