Interpretation of z-score?

Question

Can anyone tell me what does a high and a low z-score mean(if possible,in more detail please)? Can a z-score be as high as 30+ and as low as -10? If so, what does it mean? Thank you!

Answer 1

The z-score gives the raw score's deviation from the mean measured in terms of the standard deviation for the population in question. A z-score of 30 would mean a raw score equal to the mean plus 30 std deviations; a z-score of -10 would mean a raw score equal to the mean minus 10 std deviations.
In a *truly* normal distribution, the z-score can be arbitrarily high or low. Extreme values are not probable, but are not impossible: no finite interval contains all of a literally normal distribution. (There is still 0.00003 lying more than 4 SDs up from the mean. So, for example, since the SD of IQ is about 15, you'd expect to find 3 people in 100,000 scoring 160 (z = 4) or more.)

Answer 2

The z-score is really the standardized value of a distribution. The z-score can be anything, however, after the z-score is less than -3 the value under the curve is zero. Also if the z-score is greater than 3 the value under the curve is one. So the z-score can be anything, but the area under the curve to the left of the z-score is between 0 and 1.

Answer 3

The z-score is the number of standard deviations a point is off from the mean (in normally-distributed data.) The z-score can be any number, but since 99.7% of data falls between -3 and 3, you almost never see extreme values like 30 and -10. It'd be like finding a guy that's 12 feet tall.

Answer 4

Z is a standard normal distribution, that is the Normal distribution or Gaussian distribution with mean = 0 and variance = 1.
z-score denotes the areas under the standard normal distribution curve. Z-score can be any real numbers. You can check it at the below address.