Sampling bias, means, variance and standard deviation.
Example 1
The data are 1,5,9. Treat these three values as the whole population. Find the population variance.
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Answer: 332
- The mean is 5.
- Squared deviations sum to 16+0+16=32.
- Population variance divides by 3:332.
Example 2
A sample of 20 values has mean 4. One recorded value of 1 should have been 5. Find the corrected mean.
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Answer: 4.2
- Original total =20×4=80.
- The correction increases the total by 4.
- New mean =2080+4=4.2.
Example 3
A school randomly selects 80 distinct students from its complete student list, giving every group of 80 students the same chance of selection. Which sampling method is used?
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Answer: Simple random sample
- Students are selected directly from the complete population, with every sample of the required size equally likely.
- This describes a simple random sample.