Question

question 2 (1 point) a student has these scores on their assignments. the teacher is considering dropping the 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 the mean (increases, decreases) from to approximately. the median (increases, decreases) from to.

Explanation:

Step1: Calculate initial mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 10$, and $\sum_{i=1}^{10}x_{i}=0 + 40+60 + 70+75+80+85+95+95+100=700$. So the initial mean $\bar{x}_1=\frac{700}{10}=70$.

Step2: Calculate initial median

Since $n = 10$ (even - numbered data - set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. The ordered data - set is $0,40,60,70,75,80,85,95,95,100$. The $\frac{n}{2}=5$th value is $75$ and the $(\frac{n}{2}+1)=6$th value is $80$. So the initial median $M_1=\frac{75 + 80}{2}=77.5$.

Step3: Calculate new mean after removing 0

Now $n = 9$, and $\sum_{i = 1}^{9}x_{i}=40+60 + 70+75+80+85+95+95+100=620$. So the new mean $\bar{x}_2=\frac{620}{9}\approx68.89$.

Step4: Calculate new median after removing 0

Since $n = 9$ (odd - numbered data - set), the median is the $(\frac{n + 1}{2})$th ordered value. The ordered data - set without 0 is $40,60,70,75,80,85,95,95,100$. The $(\frac{9+1}{2}) = 5$th value is $80$. So the new median $M_2 = 80$.

Answer:

Blank 1: increases
Blank 2: 70
Blank 3: 68.89
Blank 4: increases
Blank 5: 77.5
Blank 6: 80