Z-Scores (Leaving Cert Mathematics): Flashcards

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Z-Scores
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Z-score definition

Measures standard deviations a data point is from the mean

Z-score formula

Z=X−μσZ = \frac{X - \mu}{\sigma}

In Z-score formula, what is XX?

The data value

In Z-score formula, what is μ\mu?

The mean of the dataset

In Z-score formula, what is σ\sigma?

The standard deviation of the dataset

Meaning of Z=0Z = 0

Data point equals the mean

Meaning of positive Z-score

Value is above the mean

Meaning of negative Z-score

Value is below the mean

Z-score application: comparing data

Allows comparison of data from different distributions

Z-score application: probabilities

Used with Z-tables to find cumulative probability

Z-score threshold for outliers

Z<−3Z < -3 or Z>3Z > 3

Purpose of Z-scores

Standardises data for comparison across datasets

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