Representing Data (Leaving Cert Mathematics): Flashcards

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The Shape of a Distribution
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Symmetrical distribution definition

Distribution with line of symmetry; both sides match perfectly

Mean, median, mode in symmetrical distribution

Mean=Median=Mode\text{Mean} = \text{Median} = \text{Mode}

Most important type of symmetrical distribution

Normal distribution

Positive skew definition

Most data at lower values, tail extends to the right

Mean, median, mode in positive skew

Mean>Median>Mode\text{Mean} > \text{Median} > \text{Mode}

Tail direction in positive skew

Right (positive direction)

Example of positive skew distribution

Income distribution in most countries

Negative skew definition

Most data at higher values, tail extends to the left

Mean, median, mode in negative skew

Mean<Median<Mode\text{Mean} < \text{Median} < \text{Mode}

Tail direction in negative skew

Left (negative direction)

Example of negative skew distribution

Exam scores when most students perform well

Which measure is pulled by the skew?

The mean is pulled in direction of the skew

The tail rule for skew

Skew is named after the direction the tail points

Example of symmetrical distribution data

Heights of people in a large random sample

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