This activity is an introduction to random sampling.
It helps to show why this process helps to give an unbiased
sample statistic.
The
students are asked to determine the average size of an alien
Blob (from the planet Blobz) using a variety of techniques.
Resources
Two
whiteboard tools can be used to analyse the data and generate
random Blobs. A worksheet
showing 100 Blobs.
A Blob
sizes sheet showing the dimensions of the 100 Blobs.
To
download:
1. Click and hold (PC users right-click).
2. Choose 'Save Target As'.
3. Choose a location to save the file then click 'Save'.
Instructions
Hand
out the worksheets face down. Tell the students the story
about the recently discovered colony of Blobs that have
arrived on Earth from the planet Blobz. Their task is to
determine the average size (measured horizontally) of a
Blob.
1.
The students can look at the 100 Blobs on the worksheet
for ten seconds. They will then estimate the average size
(mm) of a Blob. The teacher uses the boxplot
whiteboard tool to plot the students' guesses (up to
20). Enter the estimates then click on the 'next' button.
Discuss
the data set.
2.
Each student now chooses a representative sample of 10 Blobs.
Once they have made their choice, they measure the size
(horizontal width) of each Blob (in mm) and calculate the
mean size. The teachers uses the boxplot
whiteboard tool to plot the students' guesses (up to
20).
3.
Now random samples of 10 Blobs is taken. This can be done
in two ways:
Each
student generates a random number using a calculator and
then uses the Blob
sizes sheet to find out the size of the 10 random
Blobs. They then calculate the mean size of their random
sample.
or
Use
the random
Blob generator tool. The computer will generate 10
random Blobs, calculate the mean size and plot the mean
size on a number line. Press the 'next' button
to generate another random sample of 10 Blobs. Twenty
samples can be generated. Click in the bottom right hand
corner to reveal the mean size of the 100 Blobs.
The
class discusses the difference in the distributions.
Would
you have taken a random sample if you had closed your eyes
and pointed out 10 Blobs?
