Question

a student has these scores on ten assignments. the teacher is considering dropping a lowest score. what effect does eliminating the lowest value, 0, from the data set have on the mean and median? 0 40 60 70 75 80 85 95 95 100

Explanation:

Step1: Calculate the original mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 10$, and $\sum_{i=1}^{10}x_{i}=0 + 40+60 + 70+75+80+85+95+95+100=600$. So the original mean $\bar{x}_{1}=\frac{600}{10}=60$.

Step2: Calculate the new mean

After dropping the score of 0, $n = 9$, and $\sum_{i = 1}^{9}x_{i}=40+60 + 70+75+80+85+95+95+100=620$. So the new mean $\bar{x}_{2}=\frac{620}{9}\approx68.89$. The mean increases.

Step3: Calculate the original median

Since $n = 10$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered values. The $\frac{10}{2}=5$th value is 75 and the $(\frac{10}{2}+1)=6$th value is 80. So the original median $M_{1}=\frac{75 + 80}{2}=77.5$.

Step4: Calculate the new median

Since $n = 9$ (an odd - numbered data set), the median is the $(\frac{n + 1}{2})$th ordered value. $\frac{9+1}{2}=5$th value. The ordered data set without 0 is $40,60,70,75,80,85,95,95,100$, and the median $M_{2}=80$. The median increases.

Answer:

The mean and the median both increase.