Answer: 4
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Explanation:
The mode is the most frequent value. We could have all 7s, but then that would indicate the mean is 7 (instead of 6). So we can't have all 7s.
Let's say we had two copies of "7" and then some other number x where x < 7 to ensure that the mean is smaller than the mode.
Add up the three items: x+7+7 = x+14
Divide that sum over 3 to compute the mean: (x+14)/3
This mean is 6, so,
(x+14)/3 = mean
(x+14)/3 = 6
x+14 = 3*6
x+14 = 18
x = 18-14
x = 4
The missing item is 4.
The set {4,7,7} has a mean of 6 and mode of 7.
The smallest item in this set is 4.
