Statistics 1, Activity 2
The Jellyblubber colony
In the real world collecting data is time-consuming and expensive. Consequently it is not
generally practical to collect data from an entire group of interest (known as the
population), which may be people, animals or even a previously unknown form of jellyfish.
Instead we collect data from only part of the population. This is known as sampling.
Unfortunately, it is generally easier to sample badly rather than to sample well.
Unintentionally, human responses tend to introduce bias and consequently the
statistician’s remedy is to eliminate bias by eliminating human choice. This activity tackles
this problem ‘head on’ as students contrast their initial thoughts firstly against their own
choice of sample and later against a Simple Random Sample (SRS).
In this second activity dealing with data, students are introduced to a new species of
jellyfish that has been found off the Sussex coast and nicknamed ‘jellyblubbers’ by local
people. It impossible to count how many ‘jellyblubbers’ are present, but some data has
been collected and is being analysed for the purpose of answering the specific question:
‘On average, how big is a jellyblubber?’
This problem gives the students an introduction to how sampling can be used to draw
conclusions about a much larger population.
Features of this activity
 This activity introduces the Simple
Random Sample (SRS) to students and
shows why this process helps to
generate an unbiased sample.
 It also highlights that relying on our own
perceptions can be deceiving.
 Students will learn that a simple random
sample (SRS) is often the most
effective method of generating an
unbiased sample, and that intuition can
be deceptive.
 It introduces the idea of a distribution of
sample means that will be revisited
later.
 It uses a random number table.
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Materials and preparation
Introductory video (to be supplied)
Introductory PowerPoint (jellyblubbers.ppt)
Notebook file (jellyblubbers) (This is a
Smartboard file.)
Worksheet
Rulers
Random number tables
Introducing the problem
Introduce the problem through the newspaper article by using either the PowerPoint file
or Notebook file (Smartboard).
The ongoing question throughout this activity is: ‘On average, how big is a jellyblubber?’
First impressions
Hand out the worksheet
face down. Ask the students
not to look at the sheet until
they are told but tell them it
contains an accurate artist’s
impression of the colony of
jellyblubbers. Display the
second page.
Warn the students that they
will have only 5 seconds to
look at the colony which equates to the time the marine
biologists have when they look through their lens. Make sure the students understand
they have to estimate the average width of a jellyblubber measured horizontally in mm.
Now tell your students to turn over the paper and give them exactly 5 seconds to look
before telling them to turn the paper over again. Ask the students to write down their
initial estimate.
Plot their estimates on a dot plot and discuss the dataset generated. It is very important
to ask ‘Why didn’t you all get the same answer?’
Summarise the results.
It would be good idea to discuss which average is the most appropriate, but try to guide
your students towards the ‘mean’ as we want to include everyone’s estimate.
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Choosing a representative sample
Each student is now asked to choose a representative sample of 10 jellyblubbers. Once
they have made their choice, they measure the length of each blubber and calculate the
mean length. The teacher plots these values on a new dotplot, followed by a whole class
discussion of dataset and the summary statistics generated.
Choosing a Simple Random Sample (SRS)
Now the student takes an SRS of 10 blubbers, as follows. Each jellyblubber is numbered
from 1 to 100. Students generate 10 random numbers from a random number table in
the range 1 to 100. They calculate the mean length of those ten blubbers. The teacher
plots these means on a third dotplot. Each dotplot must have the same scale for
comparison purposes.
The class discusses the difference in the distributions – location, spread, outliers, etc.
The actual average length of a blubber is 19.4 cm. Which method gave the best estimate?
How accurate was it? How much spread was there around the correct value?
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Further
discussion
A student decides to generate a random sample by closing her eyes
and pointing at the sheet of blubbers randomly. She chooses the
blubber which is closest to her finger. Comment on this method of
generating an SRS.
Extension
A similar exercise can be conducted by putting a number of pieces of
string of varying lengths into a bag and having students pull out a
‘random sample’ of lengths of string. Since a longer piece is more likely
to be selected than a shorter one, the sample generated in this fashion
is likely to give a biased result – one that is too large.
References
David S. Moore, Statistics, Concepts and Controversies, 4th edition.
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