Topic Exploration Pack
Statistical Experiments
Activity 1a Fishing
These fish are representative of a large fish population. You can imagine a huge shoal of fish and these
57 fish are a representative sample of the shoal. The number on the body of each fish is its tag or
identifier. The number at the tail of each fish is its weight in kilograms.
You are going to catch 30 fish and weigh your total catch.
To do this, follow these instructions:
1.
You will need to generate 30 whole numbers between 1 and 57. You might do this by picking
numbered tickets randomly from a box or you can use a calculator or spreadsheet. It doesn’t
matter if you get the same number twice – remember, this is a large shoal of fish and there will be
lots of fish the same weight in it.
2.
Use each number to identify a fish (by looking at the numbers on the fish bodies) and write down
the weight of each fish you have caught. You should have 30 weights.
3.
Add up all the weights of the 30 fish you have caught to get your total catch.
4.
Enter your total catch into the class spreadsheet with everyone else’s catches and look at the
shape of the graph. What do you notice? How does it compare with the distribution of weights of
the individual fish? How does the mean weight of all catches compare with the mean of the
individual fish? You may think that is an easy pitfall to avoid. But is it? You may have heard of the
‘halo effect’. This is where people rate a person’s characteristics and arguments according to how
much they like the person on first impression. Isn’t it easier to accept the argument of the teachers
you like? We need to listen carefully to the argument, whoever the person is. A person isn’t right
because they are nice. Neither are they wrong because they are horrible.
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July 2015
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Activity 1b Dice
On a fair six-sided dice, each number has a one in six change of being rolled. If you roll the dice a large
number of times then you expect each number to come up about the same number of times.
1.
Roll a fair six-sided dice 30 times and record the scores.
2.
Add up the 30 scores to get a total.
3.
Enter your total into the class spreadsheet with everyone else’s totals and look at the shape of the
graph. What do you notice? How does it compare with the distribution of the individual dice
scores? How does the mean compare with the mean of the individual dice scores?
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Activity 2b Standard Deviation of Number of Heads
You have been given 10 coins.
You are going to record the number of heads you throw with different numbers of coins and find out what
happens to the standard deviation as you increase the number of coins.
Number of heads out of….
2 coins
4 coins
6 coins
8 coins
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Trial 6
Trial 7
Trial 8
Trial 9
Trial 10
Total Heads
Proportion of
Heads
When you have completed the number of trials your teacher has told you to do

calculate the total number of heads and the proportion of heads for each column

enter your results in the class spreadsheet.
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10 coins