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The average, median and mode of a list of numbers will be the same when the middle (or mean of the two middle numbers) is equal to the most common number in the list, and that number is also the mean. This assumes that the list has only a single mode.

If you arrange such a list of numbers from least to greatest, the mode value will be grouped at the middle of the list, thus becoming the median as well. The average of the non-median values will be equal to the median/mode.

Given a target mean/median/mode and a list length, you can construct an infinite number of lists that qualify.

Here are some examples:

10 10 10 10 10 (or any list of only one number)

11 12 12 12 12 13

1 2 3 4 5 5 5 6 7 8 9

Q: When is the average median and mode the same?

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range

Mean, median and mode are ways to find averages. The mode is the most common answer in a set of data. The median the number that is in the middle when the numbers are put in order. The mean is the statical average.

They are all forms of average.

Mean median mode

The normal distribution.

Related questions

The mean is the average. The median is the middle. The mode is the most common.

Mean, median, and mode are all equal in a normal distribution.

mode

Yes, the mode is the number that occurs most often. The median is the average.

Yes. For example, in the sequence {1,2,2,2,2,3,4,7} 2 is the median, and 2 is also the mode.

(10,10,30,30,30,50,50) (20,20,30,30,30,40,40) These two sets have the same mean, median and mode.

Yes it is. The normal distribution is symmetrical around the mode. Therefore the median has to be the same :)

range

Mean Median And Mode

mean median and mode

The median and mode of any number is the same number. The mode of 5 is 5, as is the median of 5. In other words, you need two or more numbers to determine the median and mode of those numbers.

In a symmetric distribution, the mean and the median are the same. Otherwise there is no relation. In symmetric distributions with only one mode, the mode will coincide with the mean and median, but otherwise there is no relation.