If each score in a set of test scores is divided by 10, describe the effect of the division on the mean, median, mode, range, and standard deviation of the set.
To describe the effect of dividing each score in a set of test scores by 10, let's examine the statistical measures one by one:
1. Mean: Dividing each score by 10 will reduce the value of every score in the set. Since the mean is the sum of all scores divided by the number of scores, dividing each score by 10 will also divide the sum by 10. Therefore, the mean of the new set will be the original mean divided by 10.
2. Median: The median is the middle value in a sorted set of scores. Dividing each score by 10 will not change the order of the scores, only their values. As a result, the middle value will also be divided by 10. Therefore, the median of the new set will also be the original median divided by 10.
3. Mode: The mode is the most frequently occurring value(s) in a set. Dividing each score by 10 does not change the number of times each value appears, only their values. Therefore, the mode of the new set will remain the same as the original set.
4. Range: The range is the difference between the highest and lowest scores in a set. Dividing each score by 10 will reduce the value of each score, which in turn reduces the difference between the highest and lowest scores. Hence, dividing by 10 will result in a decrease in the range of the new set compared to the original set.
5. Standard deviation: The standard deviation measures the dispersion or spread of the scores in a set. Dividing each score by 10 will reduce the values of all scores, which also decreases the dispersion of the scores. As a result, dividing by 10 will cause the standard deviation of the new set to be smaller than the original set.
In summary, dividing each score in a set of test scores by 10 will result in the mean and median being divided by 10 as well, while the mode remains unaffected. The range and standard deviation will both decrease proportionally.