Question

Which of the following is not true concerning the attributes of z-scores?

Multiple Choice
A.z-scores are positive for data values above the mean of the distribution.
B.z-scores are negative for data values below the mean of the distribution.
C.z-scores can be positive or negative for data values above the mean of the distribution.
D.z-scores are equal to zero for data values equal to the mean of the distribution.

Answer 1

The statement 'z-scores can be positive or negative for data values above the mean of the distribution' is incorrect because z-scores are only positive for data above the mean and negative for data below the mean.

Step-by-step explanation:

The correct answer to which statement is not true concerning the attributes of z-scores is: C.z-scores can be positive or negative for data values above the mean of the distribution. This statement is incorrect because a z-score is positive when the data value is above the mean, indicating its position to the right of the mean. Conversely, a z-score is negative when the data value is below the mean, indicating its position to the left of the mean. If a data value equals the mean, then its z-score is zero.

To summarize, a z-score is calculated to understand how many standard deviations away from the mean a particular value lies. It provides a way to compare values from different data sets with different means and standard deviations. The standard normal distribution plays a crucial role in understanding and interpreting z-scores, with a mean of 0 and a standard deviation of 1.