IDNLearn.com: Where your questions meet expert advice and community support. Get thorough and trustworthy answers to your queries from our extensive network of knowledgeable professionals.

What statistic is produced when the difference between a score and the mean is divided by the standard deviation?

A. Mode
B. Range
C. Percentile rank
D. Median
E. Z-score


Sagot :

Certainly! Let's break down the problem step-by-step:

1. Understanding the Context:
- Different statistical measures are used to describe and analyze data.
- In this question, we are looking for the appropriate measure that involves the difference between a score and the mean, divided by the standard deviation.

2. Possibilities (Options):
- A. Mode: The mode is the value that appears most frequently in a data set. It doesn't involve the mean or standard deviation.
- B. Range: The range is the difference between the highest and lowest scores in a data set. It doesn't involve the mean or standard deviation.
- C. Percentile rank: This indicates the relative standing of a value within a data set, showing what percent of the data falls below a particular score. It also doesn't directly relate to the mean and standard deviation.
- D. Median: The median is the middle value of a data set when it is ordered from least to greatest. This measure also doesn't involve calculations with the mean or standard deviation.
- E. Z-score: The z-score is a statistical measure that describes a score's relationship to the mean of the group of scores. The z-score is calculated by taking the difference between the score and the mean, and then dividing this difference by the standard deviation.

3. Identifying the Right Statistic:
- From the explanations above, it's clear that the z-score directly fits the description provided in the question. The z-score standardizes the score by addressing how many standard deviations a score is from the mean, thereby normalizing different data points on a common scale.

4. Conclusion:
- The statistic produced when the difference between a score and the mean is divided by the standard deviation is the z-score.

Therefore, the correct answer is:
E. Z-score
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.