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How is the median calculated?
- Calculation: The median is the middle value after the observations have been ordered from lowest to highest (or highest to lowest).
- (NOTE: There are an odd number of observations so no averaging of middle values is required)
The formula for the standard deviation is given below. Explain in intuitive terms how
the standard deviation is constructed and hence how it measures “average variation”.
- [1 mark] The term inside the bracket gives the difference between the actual value and the mean value
- [1 mark] This is then squared to remove the negative differences as we are only concerned with the size and not direction of the deviation, giving a measure of the total variation.
- [1 mark] It is then averaged over (n-1) observations, where there is one observation lost due to needing to use the same sample to calculate the mean used in the numerator.
When looking at an income distribution, it can be argued that individuals with income = 0 should be removed from the distribution. What would you expect to see happen to the standard deviation if those with income = 0 were removed from this data? Explain your reasoning.
- [1 mark] The standard deviation should decrease.
- [1 mark] 0 is the minimum value so by removing it, the lowest values are being removed.
- [1 mark] This would make the remaining observations closer together and therefore decrease the standard deviation.
What is the correlation coefficient?
- For every additional Rupiah a person earns per month in 2007, they are predicted to
- have earned on average 0.44 Rupiah more per month in 2000.