Understanding Z-Scores

This video tutorial explains how to measure the distance of a data value from the mean using z-scores. It covers the basics of normal distribution, mean, and standard deviation. The tutorial compares SAT and ACT scores, demonstrating why direct comparison is invalid due to different scales. It introduces z-scores as a standard measure and provides examples of calculating z-scores for various data points. The tutorial concludes by applying z-scores to SAT and ACT scores to determine which score is relatively better.

What does the standard deviation tell us about a normal distribution?

• The average value of the data set

• The lowest value in the data set

• How spread out the data is from the mean

• The highest value in the data set

Why can't SAT and ACT scores be directly compared?

• They are for different subjects

• They are administered by different organizations

• They are taken by different age groups

• They are scored on different scales

What is a z-score?

• A measure of the average value

• A measure of how far a value is from the mean in standard deviations

• A measure of the lowest value in a data set

• A measure of the highest value in a data set

If a value is one standard deviation above the mean, what is its z-score?

• 0

• 1

• 2

• -1

How do you calculate a z-score?

• Subtract the mean from the value and divide by the standard deviation

• Add the mean to the value and multiply by the standard deviation

• Subtract the standard deviation from the value and add the mean

• Multiply the mean by the value and divide by the standard deviation

What is the z-score for a value that is 2.7 standard deviations below the mean?

• 1.7

• 2.7

• -2.7

• 0

Which score is relatively higher: an SAT score with a z-score of 1.7 or an ACT score with a z-score of 1.6?

• The SAT score

• The ACT score

• Both are equal

• Cannot be determined