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Difference between revisions of "2019 AMC 8 Problems/Problem 10"

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=Problem 10=
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The diagram shows the number of students at soccer practice each weekday during last wee. After computing the mean and median vlaues, Coach discovers that there were actually <math>21</math> participants on Wednesday. Which of the following statements describes the change in the mean and median after the correction is made?
 
<asy>
 
<asy>
 
unitsize(2mm);
 
unitsize(2mm);
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}label("Number of students at soccer practice",(14,3.5));
 
}label("Number of students at soccer practice",(14,3.5));
 
</asy>
 
</asy>
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<math>\textbf{(A) }</math>The mean increases by <math>1</math> and the median does not change.
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<math>\textbf{(B) }</math>The mean increases by <math>1</math> and the median increases by <math>1</math>.
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<math>\textbf{(C) }</math>The mean increases by <math>1</math> and the median increases by <math>5</math>.
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<math>\textbf{(D) }</math>The mean increases by <math>5</math> and the median increases by <math>1</math>.
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<math>\textbf{(E) }</math>The mean increases by <math>5</math> and the median increases by <math>5</math>.
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==Solution 1==
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==See Also==
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{{AMC8 box|year=2019|num-b=9|num-a=11}}
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{{MAA Notice}}

Revision as of 17:53, 20 November 2019


Problem 10

The diagram shows the number of students at soccer practice each weekday during last wee. After computing the mean and median vlaues, 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

See Also

2019 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 9 		Followed by
Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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