For a class test, the mean score was 65, the median score was 71 and sthe standard deviation of the scores was 7. The teacher decided to add 5 points to each score due to a grading error. Which of the folloiwng must be true for thenew scores?
TH
Hmmmm. the mean is now 70, the median is now 76, and the standard deviation is 7. That is not a smart way to curve grades, usually.
To determine which of the following must be true for the new scores, we need to understand how adding 5 points affects the mean, median, and standard deviation.
1. Mean: Adding a constant value to each score will also add the same value to the mean. Therefore, the new mean score will be 65 + 5 = 70.
2. Median: Adding a constant value to each score does not affect the relative order of the scores, so it does not change the median. Therefore, the new median score will still be 71.
3. Standard Deviation: Adding a constant value to each score does not affect the standard deviation. Therefore, the new standard deviation will still be 7.
Based on this analysis, we can conclude that the new scores must have a mean of 70, a median of 71, and a standard deviation of 7. So, the correct statement is:
"The mean score is 70, the median score is 71, and the standard deviation is 7 for the new scores."
To determine which of the following must be true for the new scores, let's break down the information given step by step:
1. Mean score: The original mean score was 65. If we add 5 points to each score, the mean score will increase by 5 as well. Therefore, the new mean score will be 65 + 5 = 70.
2. Median score: The original median score was 71. Adding 5 points to each score will shift the distribution but will not change the order of the scores. Therefore, the new median score will still be 71.
3. Standard deviation: The original standard deviation of the scores was 7. Adding a constant value to each score doesn't change the standard deviation. Therefore, the new standard deviation will also be 7.
Based on these calculations, we can conclude that the following must be true for the new scores:
- The new mean score must be 70.
- The new median score must be 71.
- The new standard deviation must be 7.
Thus, option (C) is correct.