If the mean, median, and mode are all equal for the set {3,4,5,8,x}, what is the value of x?

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Answer 1 · 2016-08-20T14:32:06

#x = 5#

1st question to ask would be, " Are the values in order?"

Clearly they can't be because then #x# would have to be equal to 8 in order to have a mode of 8. But while 8 could be the mode, it is not the median.

2nd question " Where must #x# lie?"

The mode will have to be equal to the median. (the middle value).

This would lead to {3,4,5 ,x ,8} #rArr# {3,4,5, 5 ,8}

What about the mean? If #x=5#, the sum of the numbers = 25.

Mean = #25/5 = 5#