2016 AMC 10A Problems/Problem 7
(Redirected from 2016 AMC 12A Problems/Problem 4)
Problem
The mean, median, and mode of the data values are all equal to . What is the value of ?
Solution 1
Since is the mean,
Therefore, , so
Solution 2
Note that must be the median so it must equal either or . You can see that the mean is also , and by intuition should be the greater one. ~bjc
Check
Order the list: . must be either or because it is both the median and the mode of the set. Thus is correct.
Video Solution
https://youtu.be/XXX4_oBHuGk?t=163
~IceMatrix
~savannahsolver
See Also
2016 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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 AMC 10 Problems and Solutions |
2016 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 3 |
Followed by Problem 5 |
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 AMC 12 Problems and Solutions |
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