Question

If all the values in a data set are convertedto z-scores, the shape of the distribution of the z-scores will be the same as the distribution of the original data. True or false?

Answer 1

Given statement, " If all the values in a data set are converted to z-scores, the shape of the distribution of the z-scores will be the same as the distribution of the original data." is True

Note:  If every x value is transformed into a z-score, then the distribution of z-scores will have following properties regarding shape, mean, and standard deviation,

distribution of z-scores will have exactly the same shape as original distribution of scores; z-score mean will always have mean of 0 & z-scores will always have standard deviation of 1.