Question

multiple choice
at the end of the semester, mrs. johnson allows her students to drop their low - est test score.
if jonah drops his lowest test score at the end of the semester, which of the fol - lowing statements is most likely true?
remember:
removing an extreme value (outlier) has the greatest effect on the mean and range of a data set.
a jonahs average test score will increase.
b the range of jonahs test scores will remain unchanged.
c jonahs median test score will decrease.

Explanation:

Step1: Analyze the effect on the mean

The mean is calculated by summing all the scores and dividing by the number of scores. When the lowest score (which is a relatively small value) is dropped, the sum of the remaining scores increases (since we are removing a small value), and the number of scores decreases by 1. The net effect is that the mean (average) will increase. For example, if the scores are \(20,80,90\), the mean is \(\frac{20 + 80+90}{3}=\frac{190}{3}\approx63.33\). If we drop \(20\), the new mean is \(\frac{80 + 90}{2}=85\).

Step2: Analyze the effect on the range

The range is the difference between the highest and the lowest score. When the lowest score is dropped, the new lowest score among the remaining scores is higher than the original lowest score. So the range (highest - lowest) will decrease. For example, if scores are \(20,80,90\), range is \(90 - 20=70\). After dropping \(20\), scores are \(80,90\), range is \(90 - 80 = 10\).

Step3: Analyze the effect on the median

If the number of scores \(n\) is odd, say \(n = 2k+1\) (original scores), and after dropping one score \(n'=2k\). For example, if scores are \(20,80,90\) (median is \(80\)), after dropping \(20\), scores are \(80,90\) (median is \(\frac{80 + 90}{2}=85\) which is an increase. In general, when we remove the lowest value, the median may increase or stay the same (if there are multiple lowest - like scores \(20,20,80,90\), original median of \(\frac{20 + 80}{2}=50\), after dropping one \(20\): scores \(20,80,90\), median is \(80\)). It will not decrease.

Answer:

A. Jonah's average test score will increase.