MathDB

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(1 cm);
real unitwidth, dayheight, barheight; int i;
unitwidth = 0.5; dayheight = 1; barheight = 0.3;
draw((unitwidth,0)--(unitwidth,5*dayheight),gray(0.7)); draw((2*unitwidth,0)--(2*unitwidth,5*dayheight),gray(0.7)); draw((3*unitwidth,0)--(3*unitwidth,5*dayheight),gray(0.7)); draw((4*unitwidth,0)--(4*unitwidth,5*dayheight),gray(0.7)); draw((5*unitwidth,0)--(5*unitwidth,5*dayheight),gray(0.7)); draw((6*unitwidth,0)--(6*unitwidth,5*dayheight),gray(0.7)); draw((7*unitwidth,0)--(7*unitwidth,5*dayheight),gray(0.7));
fill((0,1/2*dayheight - 1/2*barheight)--(8*unitwidth,1/2*dayheight - 1/2*barheight)--(8*unitwidth,1/2*dayheight + 1/2*barheight)--(0,1/2*dayheight + 1/2*barheight)--cycle,gray(0.5));
fill((0,5/2*dayheight - 1/2*barheight)--(8*unitwidth,5/2*dayheight - 1/2*barheight)--(8*unitwidth,5/2*dayheight + 1/2*barheight)--(0,5/2*dayheight + 1/2*barheight)--cycle,gray(0.5));
draw((8*unitwidth,0)--(8*unitwidth,5*dayheight),gray(0.7)); draw((9*unitwidth,0)--(9*unitwidth,5*dayheight),gray(0.7));
fill((0,9/2*dayheight - 1/2*barheight)--(10*unitwidth,9/2*dayheight - 1/2*barheight)--(10*unitwidth,9/2*dayheight + 1/2*barheight)--(0,9/2*dayheight + 1/2*barheight)--cycle,gray(0.5));
draw((10*unitwidth,0)--(10*unitwidth,5*dayheight),gray(0.7));
fill((0,3/2*dayheight - 1/2*barheight)--(11*unitwidth,3/2*dayheight - 1/2*barheight)--(11*unitwidth,3/2*dayheight + 1/2*barheight)--(0,3/2*dayheight + 1/2*barheight)--cycle,gray(0.5));
draw((11*unitwidth,0)--(11*unitwidth,5*dayheight),gray(0.7)); draw((12*unitwidth,0)--(12*unitwidth,5*dayheight),gray(0.7));
fill((0,7/2*dayheight - 1/2*barheight)--(13*unitwidth,7/2*dayheight - 1/2*barheight)--(13*unitwidth,7/2*dayheight + 1/2*barheight)--(0,7/2*dayheight + 1/2*barheight)--cycle,gray(0.5));
draw((0*unitwidth,0)--(0*unitwidth,5*dayheight),gray(0.7)); draw((13*unitwidth,0)--(13*unitwidth,5*dayheight),gray(0.7)); draw((14*unitwidth,0)--(14*unitwidth,5*dayheight),gray(0.7));
label("

0

", (0,5*dayheight), N); label("

4

", (2*unitwidth,5*dayheight), N); label("

8

", (4*unitwidth,5*dayheight), N); label("

12

", (6*unitwidth,5*dayheight), N); label("

16

", (8*unitwidth,5*dayheight), N); label("

20

", (10*unitwidth,5*dayheight), N); label("

24

", (12*unitwidth,5*dayheight), N); label("

28

", (14*unitwidth,5*dayheight), N); label("Number of students at soccer practice", (7*unitwidth,6*dayheight)); label("Monday", (-0.5*unitwidth,9/2*dayheight), W); label("Tuesday", (-0.5*unitwidth,7/2*dayheight), W); label("Wednesday", (-0.5*unitwidth,5/2*dayheight), W); label("Thursday", (-0.5*unitwidth,3/2*dayheight), W); label("Friday", (-0.5*unitwidth,1/2*dayheight), W); [/asy]

<span class='latex-bold'>(A) </span> \text{The mean increases by 1 and the median does not change.}

<span class='latex-bold'>(B) </span> \text{The mean increases by 1 and the median increases by 1.}

<span class='latex-bold'>(C) </span> \text{The mean increases by 1 and the median increases by 5.}

<span class='latex-bold'>(D) </span> \text{The mean increases by 5 and the median increases by 1.}

<span class='latex-bold'>(E) </span> \text{The mean increases by 5 and the median increases by 5.}

Problem Statement