Difference between revisions of "2016 AMC 8 Problems/Problem 6"
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The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these names? | The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these names? | ||
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<asy> | <asy> | ||
unitsize(0.9cm); | unitsize(0.9cm); | ||
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label("name length", (4.5, -1)); | label("name length", (4.5, -1)); | ||
</asy> | </asy> | ||
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| + | <math>\textbf{(A) }3\qquad\textbf{(B) }4\qquad\textbf{(C) }5\qquad\textbf{(D) }6\qquad \textbf{(E) }7</math> | ||
==Solutions== | ==Solutions== | ||
Revision as of 09:37, 23 September 2021
Problem
The following bar graph represents the length (in letters) of the names of 19 people. What is the median length of these names?
![[asy] unitsize(0.9cm); draw((-0.5,0)--(10,0), linewidth(1.5)); draw((-0.5,1)--(10,1)); draw((-0.5,2)--(10,2)); draw((-0.5,3)--(10,3)); draw((-0.5,4)--(10,4)); draw((-0.5,5)--(10,5)); draw((-0.5,6)--(10,6)); draw((-0.5,7)--(10,7)); label("frequency",(-0.5,8)); label("0", (-1, 0)); label("1", (-1, 1)); label("2", (-1, 2)); label("3", (-1, 3)); label("4", (-1, 4)); label("5", (-1, 5)); label("6", (-1, 6)); label("7", (-1, 7)); filldraw((0,0)--(0,7)--(1,7)--(1,0)--cycle, black); filldraw((2,0)--(2,3)--(3,3)--(3,0)--cycle, black); filldraw((4,0)--(4,1)--(5,1)--(5,0)--cycle, black); filldraw((6,0)--(6,4)--(7,4)--(7,0)--cycle, black); filldraw((8,0)--(8,4)--(9,4)--(9,0)--cycle, black); label("3", (0.5, -0.5)); label("4", (2.5, -0.5)); label("5", (4.5, -0.5)); label("6", (6.5, -0.5)); label("7", (8.5, -0.5)); label("name length", (4.5, -1)); [/asy]](http://latex.artofproblemsolving.com/7/3/9/7396694d92e8f9794065daafaf571852434d0b08.png)
Solutions
Solution 1
We first notice that the median name will be the 
name. The name is 
.
Solution 2
To find the median length of a name from a bar graph, we must add up the number of names. Doing so gives us 
. Thus the index of the median length would be the 10th name. Since there are 
names with length 
, and names with length 
, the 
th name would have letters. Thus our answer is .
See Also
| 2016 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
