# Problem 10

The diagram shows the number of students at soccer practice each weekday during last week. After computing the mean and median values, Coach discovers that there were actually $21$ participants on Wednesday. Which of the following statements describes the change in the mean and median after the correction is made? $[asy] unitsize(2mm); defaultpen(fontsize(8bp)); real d = 5; real t = 0.7; real r; int[] num = {20,26,16,22,16}; string[] days = {"Monday","Tuesday","Wednesday","Thursday","Friday"}; for (int i=0; i<30; i=i+2) { draw((i,0)--(i,-5*d),gray); }for (int i=0; i<5; ++i) { r = -1*(i+0.5)*d; fill((0,r-t)--(0,r+t)--(num[i],r+t)--(num[i],r-t)--cycle,gray); label(days[i],(-1,r),W); }for(int i=0; i<32; i=i+4) { label(string(i),(i,1)); }label("Number of students at soccer practice",(14,3.5)); [/asy]$ $\textbf{(A) }$The mean increases by $1$ and the median does not change. $\textbf{(B) }$The mean increases by $1$ and the median increases by $1$. $\textbf{(C) }$The mean increases by $1$ and the median increases by $5$. $\textbf{(D) }$The mean increases by $5$ and the median increases by $1$. $\textbf{(E) }$The mean increases by $5$ and the median increases by $5$.

## Solution 1

On Monday, 20 people come. On Tuesday, 26 people come. On Wednesday, 16 people come. On Thursday, 22 people come. Finally, on Friday, 16 people come. 20+26+16+22+16=100, so the mean is 20. The median is (16,16,20,22,26) 20. The coach figures out that actually 21 people come on Wednesday. The new mean is 21, while the new median is (16,20,21,22,26)21. The median and mean both change, so the answer is $\boxed{\textbf{(B)}}$~heeeeeeheeeee

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