Question

A set of data has a mean of 12 and a standard deviation of 3. A data point of the set has a z-score of 1.3. What does a z-score of 1.3 mean?

The data point is 1.3 standard deviations away from 3

The data point is 1.3 standard deviations away from 12.

The data point is 3 standard deviations away from 1.3.

The data point is 3 standard deviations away from 12.

Answer 1

The second option. The data point is 1.3 standard deviations away from 12.

Answer 2

How?

Answer 3

The formula for z-score is (point - mean)/standard deviation.

What the z-score calculates is how far away a point is from the mean. Let's say we selected a point that had a value of 15. Well that would mean with the z-score formula you'd do (15-12)/3 which equals 1. Meaning the z-score is equal to 1 which makes perfect sense because 15 is exactly 1 standard deviation away from the mean.

So something that has a z-score of 1.3 means it is 1.3 standard deviations away from the mean. Since the mean is 12, that means a point with a z-score of 1.3 is 1.3 standard deviations away from 12.

Does that make sense?

Answer 4

Yes it does. Thank you so much