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All 9 Flashcards — z-values
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Question
State the standardising formula.
Answer
z = (x − μ)/σ.
Question
What does a z-value tell you?
Answer
How many standard deviations x is above (z > 0) or below (z < 0) the mean.
Question
What does z = 0 mean?
Answer
The value equals the mean.
Question
What does a negative z-value indicate?
Answer
The value is below the mean.
Question
Why are z-values useful for comparing?
Answer
They put values from different normal distributions on a common (standardised) scale.
Question
Across two distributions, which result is relatively better?
Answer
The one with the larger z-value (further above its own mean).
Question
What is the standard normal distribution?
Answer
Z ~ N(0, 1) — mean 0 and standard deviation 1.
Question
Does a z-value have units?
Answer
No — it is a count of standard deviations, so it is unitless.
Question
x is 2σ above the mean. What is z?
Answer
z = 2.
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Full study notes for z-values
Topic 4.12 hub
z-values & inverse normal
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