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Sample size and variation
Consider the following data collected from tossing a coin 10 times (sample size 10) and recording the result as H (head) or T (tail).
The coin toss is conducted 5 times and the percentage of heads calculated.
1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | 10th | % H |
T | H | T | H | T | H | T | H | H | T | 50 |
T | H | T | T | T | H | T | H | T | T | 30 |
H | T | H | T | T | H | H | H | H | H | 70 |
H | T | H | T | T | T | T | H | T | H | 40 |
H | H | H | T | H | T | H | H | H | H | 80 |
The outcomes vary from 30% to 80%.
The following results are from 5 samples of 100 tosses of the coin.
Number of tosses | % H |
100 | 50 |
100 | 49 |
100 | 50 |
100 | 54 |
100 | 47 |
The outcomes vary from 47% to 54%.
The variation from the expected 50% heads is much less for 100 tosses than for 10 tosses.
Variation in sample size for coin tosses
Sample size is important for obtaining reliable data. This activity uses technology to produce many trials.
Sampling from a mystery population
When sampling to determine the nature of an unknown population, reliability increases as sample size increases. In this activity, the sample size is steadily increased and the results compared.
Random or not
This activity is based on a digital learning object which shows that the results of random samples often vary from the expected results. Conclusions based on small random sample sizes can be inaccurate because they are not necessarily representative of the entire distribution.