Using Z-Scores to Compare Data (HSC SSCE Mathematics Standard): Quizzes

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Using Z-Scores to Compare Data
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What is the main purpose of using z-scores when comparing data?

To compare datasets with different means

What is the correct formula for calculating a z-score?

z=xxˉsz = \frac{x - \bar{x}}{s}

What does a z-score tell us about a data value?

How many SDs it is from the mean

In which situation does a more negative z-score represent better performance?

Race times in swimming events

Which z-score represents a value furthest from the mean?

z=3z = -3

What does a positive z-score indicate?

The value is above the mean

Calculate the z-score: x=80x = 80, mean =70= 70, SD =5= 5.

z=2z = 2

Ali scored 65 (mean 52, SD 9.5) in English and 61 (mean 47, SD 7.5) in Maths. Which is better?

Maths with higher z-score

Why is comparing raw scores without z-scores problematic?

Like comparing apples to oranges

In swimming, David's butterfly z-score was 3-3. What does this mean?

3 SDs below mean (faster than average)

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