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24 May 2012, 13:04
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From my understanding, mean = median if,
1. the set consists of evenly spaced numbers
2. if all the members of the set are equal
3. set has just one number
Is there any thing else? In DS type of "is mean = median" questions, what do you have to know to be sure that mean = median?
1. the set consists of evenly spaced numbers
2. if all the members of the set are equal
3. set has just one number
Is there any thing else? In DS type of "is mean = median" questions, what do you have to know to be sure that mean = median?
31 May 2012, 12:03
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Perhaps the easiest way to understand when mean = median is this one reqiurement:
1) When the distribution above the mean is symmetrical to the distribution below the mean.
So think of the middle point. Whatever pattern of data you have above the middle point is mirrored on the other side (below) the middle point.
When this happens, the mean will effectively be the same as the median (the middle number by rank).
This is satisfied when data is evenly spaced out. It's also true in other mirror-like cases.
Sure the distribution does not necessarily have to be exactly mirrored on both sides. But as long as they roughly cancel each other out, then you'll have a situation where the mean = median.
1) When the distribution above the mean is symmetrical to the distribution below the mean.
So think of the middle point. Whatever pattern of data you have above the middle point is mirrored on the other side (below) the middle point.
When this happens, the mean will effectively be the same as the median (the middle number by rank).
This is satisfied when data is evenly spaced out. It's also true in other mirror-like cases.
Sure the distribution does not necessarily have to be exactly mirrored on both sides. But as long as they roughly cancel each other out, then you'll have a situation where the mean = median.
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Joined: 21 May 2012
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Not true, here's an example where mean = median and none of your criteria listed are met.
{0,50,50,50,100}
For any evenly spaced set, the mean of the set is always equal to the median. But not vice versa!
{0,50,50,50,100}
For any evenly spaced set, the mean of the set is always equal to the median. But not vice versa!
