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Can a mean average ever be higher than a median average?
Yes. If the predominant data are higher than the median, the mean average will be higher than the median average. For example, the median average of the numbers one through ten is five. The mean average is five and one-half.
What is five numbers that have a range of 10 a median of 7 and mean of 6?
If the mean is 6 then the 5 numbers must total 6 * 5 = 30. Median is 7, so that leaves 4 numbers totaling 23. So we need 2 numbers less than (or equal to) 7 and 2 numbers greater than (or equal to) 7 which all add up to 23 and where the highest number minus the lowest number equals 10. So how about, 1,2,7,9,11 or 1,1,7,10,11 etc
Is the mean equal to the median if the data set consist of 1000 values that are all different?
No. Not necessarily. Here are two examples with a smaller set of numbers: A) 1, 2, 3, 4 Mean: 10/4 = 2.5 Median: the mean of the two central elements - also 2.5. B) 1, 2, 3, 394 Mean: 400 / 4 = 100 Median: the mean of the two central elements = 2.5. You can extend the same principle - of having numbers on side of the center farther from the center than the numbers on the other side - to get a different mean and median, for sets of just about any size.
What does the median tell you?
The median is the middle number of any given set when they are in order, least to greatest. If there is an even number of values, the median is the average of the middle two. It tells you that half the members of the set are greater than it and half are less than it.
What is the definition of median?
That means that, in a set of numbers, there are just as many numbers greater than the calculated median, as there are numbers less than the median. To calculate the median, sort the numbers, then pick the number in the middle. If there are two middle numbers, take their average.
