You can clearly see the shape of the distribution without any of the original data being lost
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What are histograms good for?
When frequency tables have unequal class widths
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Mode is...
Easy to calculate and isn't affected by extreme values, but has no useful mathematical properties.
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Median is...
Easy to calculate and isn't affected by extreme values, and has a restricted use
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Mean is...
Very important for mathematical properties but can be affected by extreme values as it makes use of all values
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IQR is...
Easy to calculate and is not affected by extreme values, but has no mathematical properties that are useful
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Standard Deviation measures...
The spread of the data, is affected by extreme values but NOT addition/subtraction after coding!
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NEGATIVE SKEW
MODE>MEDIAN>MEAN Q2-Q1>Q3-Q2
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What do box plots show?
The range, IQR, median and skewness, so are good for comparing
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How do you know when data is a DISCRETE RANDOM VARIABLE, X?
The probabilities add up to 1
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E(aX+b) =
aE(X) + b
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Var(aX+b) =
a^2VarX
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A DISCRETE UNIFORM DISTRUBUTION is...
When each value has an equal probability. Eg, a dice.
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What is a summary statistic?
Mean and SD or Median and IQR.
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Choose mean and SD when...
Data isn't skewed and extreme values aren't present to make use of all the data
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Choose median and IQR when...
when data is skewed and extreme values are present
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Forming a statistical model...
1. Observe real world problem. 2. Devise a statistical model and collect data. 3. Compare observed outcomes against expected outcomes and test model. 4. Refine model if necessary and test again.
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PROS/CONS of a statistical model...
PROS - quick, cheap, enables predictions. CONS - does not replicate the real world situation in every detail.
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What is a statistical experiment?
A test/investigation/process adopted for collecting data to provide evidence for/against a hypothesis
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4 Features of a normal distribution
1. Bell shaped curve, 2. Symmetrical about mean, 3. mean=median=mode, 4.95% of data lies within 2SDs of the mean
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The independent variable is...
EXPLANATORY - it is independent of the other variable and is plotted along the x axis
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The dependent variable is...
RESPONSE - it is dependent of the independent variable and is plotted along the y axis.
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