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Chapter 12: Problem 81

Describe when a \(z\)-score is negative.

Short Answer

Expert verified
A z-score is negative when the observed data point is less than the mean of a group of data points. It indicates that the data value is below the mean.

Step by step solution

01

Understanding z-score

A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the data value is higher than the mean; and a negative z-score signifies it is below the mean.
02

Explaining Negative z-score

A z-score is negative when the observed value or data point is less than the mean average. This happens because when calculating the z-score, we subtract the mean from the observed value. If the observed value is less than the mean, the result before dividing by the standard deviation is negative, thus the z-score is negative. The more negative the Z score, the further below the mean the observation is.

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Most popular questions from this chapter

Two classes took a statistics test. Both classes had a mean score of 73 . The scores of class A had a standard deviation of 5 and those of class B had a standard deviation of 10 . Discuss the difference between the two classes' performance on the test.

The scores on a test are normally distributed with a mean of 100 and a standard deviation of 20.Find the score that is 1 standard deviation below the mean.

What is a symmetric histogram?

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8.Convert each data item to a z-score. 48

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8.Convert each data item to a z-score. 76
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