Answer :
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
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
