mean = median means the set is equally spaced? if so, why are the numbers not evenly spaced in the question? Thank you everyone.
Mean = median --> evenly spaced question
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(1) 7 < x < 11
Arranging the numbers in ascending order, we get, 2, 7, x, 11, 16, which clearly implies that x is the median.
Mean = (2 + 7 + x + 11 + 16)/5 = (36 + x)/5
Now, mean = median implies (36 + x)/5 = x
Solving we get, 4x = 36 or x = 9; SUFFICIENT.
(2) x is the median of 5 numbers.
The same calculation as in statement 1 follows; SUFFICIENT.
The correct answer is D.
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I have read numerous times that when the mean equals the median, the set is equally spaced, right? If this set is equally spaced, the numbers do not add up. There is 5 between 2 and 7, 4 between 7 and 11, and 5 between 11 and 16. So, the set is not equally spaced but the median = average?
[quote="Anurag@Gurome"][quote="myfish"]mean = median means the set is equally spaced? if so, why are the numbers not evenly spaced in the question? Thank you everyone.
[url=https://postimage.org/image/z33d1msk/][img]https://s4.postimage.org/z33d1msk/PS_8_35.jpg[/img][/url][/quote]
(1) 7 < x < 11
Arranging the numbers in ascending order, we get, 2, 7, x, 11, 16, which clearly implies that x is the median.
Mean = (2 + 7 + x + 11 + 16)/5 = (36 + x)/5
Now, mean = median implies (36 + x)/5 = x
Solving we get, 4x = 36 or x = 9; SUFFICIENT.
(2) x is the median of 5 numbers.
The same calculation as in statement 1 follows; SUFFICIENT.
The correct answer is [spoiler]D[/spoiler].[/quote]
[quote="Anurag@Gurome"][quote="myfish"]mean = median means the set is equally spaced? if so, why are the numbers not evenly spaced in the question? Thank you everyone.
[url=https://postimage.org/image/z33d1msk/][img]https://s4.postimage.org/z33d1msk/PS_8_35.jpg[/img][/url][/quote]
(1) 7 < x < 11
Arranging the numbers in ascending order, we get, 2, 7, x, 11, 16, which clearly implies that x is the median.
Mean = (2 + 7 + x + 11 + 16)/5 = (36 + x)/5
Now, mean = median implies (36 + x)/5 = x
Solving we get, 4x = 36 or x = 9; SUFFICIENT.
(2) x is the median of 5 numbers.
The same calculation as in statement 1 follows; SUFFICIENT.
The correct answer is [spoiler]D[/spoiler].[/quote]
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No, that's backwards. When a set is equally spaced, then yes, the mean and median are always equal. But the reverse is not necessarily true. For example, in the set below, the mean and median are equal:myfish wrote:mean = median means the set is equally spaced?
0, 1, 50, 99, 100
but the set is certainly not equally spaced.
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