Question

Suppose that all the values in a data set are converted to z scores. Which of the statements below is true?

The mean and standard deviation of the z scores will be the same as the mean and standard deviation of the original data values.

The mean of the z scores will be zero, and the standard deviation of the z scores will be the same as the standard deviation of the original data values.

The mean and the standard deviation of the z scores will both be 0.

The mean of the z scores will be 0, and the standard deviation of the z scores will be 1.

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Answer 1

The mean of the z scores will be 0, and the standard deviation of the z scores will be 1.

Explanation:

When the data is converted to z-scores the mean and standard deviation no longer stay the same. Both these quantities are transformed into news values.

Values converted to z scores follow a standard Normal curve. This curve is symmetric about the mean. The mean of standard normal curve is 0 with a standard deviation of 1.

Therefore, the correct answer is:

The mean of the z scores will be 0, and the standard deviation of the z scores will be 1.