AP Statistics
Ch 12 – Rolling Down the River
Name _____________________________
Date _______________________ Hr ____
A farmer has just cleared a new field for corn. It is a unique plot of land in that a river runs along one
side. The corn looks good in some areas of the field but not others. The farmer is not sure that harvesting
the field is worth the expense, but he remembers reading in one of his farming magazines about a guy
that took a sample of his field in order to estimate the true total yield of the crop. The farmer has decided
to try this and wants to harvest 10 plots and use this information to estimate the total yield. Based on this
estimate, he will decide whether to harvest the remaining plots.
Convenience Sample
The article that the farmer read did not give much information about how to choose which plots to sample,
and the farmer really doesn’t want to put a lot of time and wasted energy if the corn crop is bad. He
decides to make life easy for himself and chooses the 10 plots that are closest to his house and therefore
easiest to harvest. They are marked below on the aerial view of the farmer’s land:
Do you think this method will produce good results? Why or why not?
The farmer’s wife, a very wise woman, doesn’t think her husband’s method will produce a good estimate
of the corn crop. She suggests to the farmer that he contact the math department at the local high school
and see if there’s someone that could help determine the approximate yield of the field. (That’s you!) As
the farmer’s (very inexpensive) consultant, you will be allowed to pick 10 plots to harvest early and your
task is to determine which of the following methods is the best one to use – and to decide if this is an
improvement over the farmer’s original plan.
Simple Random Sample
A simple random sample is like pulling names from a hat. However, there are obvious issues with putting
plots of land into a hat, so other methods must be devised. Most of the time, these methods involve a
“random number generator” to randomly pick “names” from the “hat”. Make sure to “name” each plot
with a numbering scheme first!! Use your calculator or a random number table to choose 10 plots to
harvest. Mark them on the grid below, and describe your method of selection.
Describe your method here:
Are there any advantages or disadvantages to this method?
Stratified Random Sample
A stratified random sample puts the entire population into smaller groups (“hats”), then randomly drawing
a name(s) from each “hat”. The key to stratified sampling are the groups, which are called strata. Each
stratum contains a group of like objects, like a “hat” of apples and a “hat” of oranges and a “hat” of
bananas. Notice that each group is made of like objects, but the groups themselves are very different. For
our farmer’s field, we must first decide what use for the strata in this situation, and then use our random
number generator to randomly pick a “name” from each “hat”. Again, make sure to use an appropriate
numbering scheme!! Use your calculator or a random number table to randomly choose one plot from
each stratum, mark these plots on the grid, and describe your method of selection.
Describe your method here, including your strata:
Are there any advantages or disadvantages to this method?
Cluster Sample
A cluster sample is similar to a stratified sample in that it also breaks the population into smaller groups.
However, it differs in that we want the groups themselves to be similar to each other, so that every group
looks more or less like the other groups, like mixed bags of fruit. With clusters, every “hat” looks alike so
you only have to pick one “hat” and let it represent the entire population. For our farmer’s field, we again
need to decide what our “hats” are, and then use a random number generator to randomly pick a single
“hat” to represent the entire field. Use your calculator or a random number table to randomly choose one
“hat”, mark the plots on the grid, and as always, describe your method below.
Describe your method here:
Are there any advantages or disadvantages to this method?
Let’s harvest some corn!!!
OK, the crop is ready. Mrs. Temple will provide you with the yield per plot for the entire field. For each
sampling method above, identify the plots you randomly chose and determine the total actual crop yield
for your 10 plots. Then use that total to determine an estimate of the average yield of a single plot of
corn and finally determine an estimate for the total corn harvest of the entire field.
Sampling Method
Convenience Sample (Farmer’s)
Mean yield per plot
Estimate of total yield
Simple Random Sample
Stratified Random Sample
Cluster Sample
**Adapted from NCSSM Statistics Leadership Institute, July 2000 by Shelli Temple, July 2010**
Observations:
1) You have looked at four different methods of choosing plots. Is there a reason, other than
convenience, to choose one method over another?
2) How did your estimates vary according to the different sampling methods you used?
3) Compare your results to someone else in the class. Were your results similar?
4) Pool the results of all students for the mean yields from the simple random samples and make a
class boxplot. Repeat for means from stratified and cluster. Compare the class boxplots for each
sampling method. What do you see?
5) Which sampling method should you use? Why do you think this method is best?
6) What was the actual yield of the farmer’s field? How did the boxplots relate to this actual value?
(Actual was 5004)
Teacher Notes:
Have students put their numerical results on the board for discussion, then when get to graphical displays,
use this data to make boxplots and write comparisons.
The above questions can be used as class discussion or journal prompts.
@JamiDanielle suggested creating a picture of the examples for stratified and cluster and putting on the
whiteboard…