Question

decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). explain your reasoning. in a data set of 10 exam scores, in which no two people got the same score, the mean was equal to the score of the person with the third - highest grade. choose the correct answer below. a. the statement does not make sense because the mean is always the middle of the data set. b. the statement does not make sense because for a data set of 10 exam scores with no repeated scores, the mean will always be equal to the average of the fifth lowest and fifth highest grades. c. the statement makes sense because the data could be skewed towards the higher scores, causing the mean to be equal to the third highest grade. d. the statement makes sense because the data could be skewed towards the lower scores, causing the mean to be equal to the third highest grade.

Explanation:

The mean of a data - set is not always in the middle of the data - set or equal to a particular value in the data - set. In a skewed data - set, the mean can be pulled in the direction of the skew. Just because no two people got the same score in a data set of 10 exam scores does not mean the mean will be equal to the third - highest score. The mean is calculated by summing all the values and dividing by the number of values, and its position relative to individual data points depends on the distribution of the data.

Answer:

A. The statement does not make sense because the mean is not always the middle of the data set.