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19 Cards in this Set
- Front
- Back
Mathematical models are useful because:
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They are quick and easy to produce
They can simplify a more complex situation They can help us improve our understanding of the real world as certain variables can readily be changed They enable predictions to be made They can help us to provide control - as in aircraft scheduling |
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Mathematical models should be treated with caution because:
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The model is a simplification of the real world problem and does not include all aspects of the problem
The model may only work in certain situations |
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Outline the steps to design a mathematical model
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1). Observe a real world problem
2). Devise a mathematical model 3). Make predictions about the expected behaviour of the real world problem using the mathematical model 4). Collect experimental data from the real world 5). Compare predicted and observed outcomes 6). Use a statistical test to assess how well the model describes the real world 7). Refine the mathematical model if necessary to improve the match of predicted outcomes with observed (experimental) data |
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What is your understanding of a statistical model?
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It is a process of statistical analysis
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What is an event?
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A set of possible outcomes in a statistical experiment
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Frequency Density =
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Frequency / Class Width
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Equation for p(x) when referring to discrete uniform data
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p(x) = 1/n
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Equation for E(X) when referring to discrete uniform data
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E(X) = (n+1)/2
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Equation for Var(X) when referring to discrete uniform data
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Var(X) = (n^2 - 1) / 12
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Key features of normally distributed data
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1) Only used with continuous data
2) Perfectly symmetrical about the mean 3) Horizontal axis asymptotic to the curve 4) Distribution is bell shaped 5) 68.3% of the data lies within 1 standard deviation of the mean 6) 95% of the data lies within 2 standard deviations of the mean 7) 99% of the data lies within 3 standard deviations of the mean |
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How does coding affect the mean?
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Addition, subtraction, multiplication and division affects the mean
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How does coding affect the variance/ standard deviation?
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Affected by multiplication and division.
Not affected by addition or subtraction as it does not affect the spread of the data. |
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How does coding affect the product moment correlation coefficient?
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Not affected at all
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How do you convert a coded regression line to its uncoded version?
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Substitute original expressions into coded regression line
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Comment on the range in the comparison of data sets
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1) Gives a rough idea on spread
2) Affected by extreme values 3) Generally used on small data groups 4) Used with median or mode |
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Comment on the IQR in the comparison of data sets
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1) Not affected by extreme values
2) Often used with median 3) Used when data is skewed |
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Comment on the mean and standard deviation in the comparison of data sets
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1) Generally used when data are fairly symmetrical (i.e little or no skew)
2) Used when data group is large |
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Criteria for normal distribution to be suitable
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All data should lie within 2 standard deviations of the mean
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What is the limitation of the product moment correlation coefficient?
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Even if two variables are associated and have linear correlation, it does not necessarily mean that a change in one of the variables causes a change in the other variable
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