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.

Question

Mathematics

Emerson Bridges

18 November, 05:50

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.

+1

Answers (1)

Know the Answer?

Brooklynn Osborn · Answer 1

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

Step-by-step 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.