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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