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No, not necessarily. They each measure central tendency but in different ways. The mean measures the average of all of the scores while the mean is the middle score. In a normal distribution the median and mean must be equal. In other data sets, they may or may not be equal.

For example, the set {0, 1, 2, 3, 5, 7, 10} has a mean of 28/7 = 4 and a median of 3.

Q: Are the median and the mean always the same value?

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Yes they can. That is why we have them. We would not need both if they always gave the same value. A mean is the total of numbers divided by the amount of numbers. A median is the middle value in the list when it is in numerical order. Usually they are similar, but not always the same. If there is an extreme number, much different than all the others, then the mean and median will be very different. Take 1, 3, 4, 7, 900. 4 is the Median. 183 is the mean. 183 is not very representative of the set, which is why a median actually works better here.

That would provide some evidence that the distribution is symmetric about the mean (or median).

Your single number is your only information of the median value of the population, so the median value is the same as your single number. It is also the mode and mean of your sample.

If there are an odd # of consecutive numbers, they will. If there are an even # of numbers, the mean will be halfway between the two medians.

No, not always. Sometimes they are equal. Sometimes they are close to each other, but not exactly the same. Sometimes they are very different. It depends on the numbers that are being used to calculate the mean and median. The way each is calculated is different. The mean is got by adding all the numbers and dividing by the amount of numbers. The median is got by arranging the numbers in order and finding the middle value in the list, if there is an odd amount of numbers, or the value half way between the two middle values when there are an even amount of numbers.

Related questions

Yes because if the numbers are all the same they can be both mean and median but they do not have to be the same.

5,6,7

Yes they can. That is why we have them. We would not need both if they always gave the same value. A mean is the total of numbers divided by the amount of numbers. A median is the middle value in the list when it is in numerical order. Usually they are similar, but not always the same. If there is an extreme number, much different than all the others, then the mean and median will be very different. Take 1, 3, 4, 7, 900. 4 is the Median. 183 is the mean. 183 is not very representative of the set, which is why a median actually works better here.

Only if the distribution is roughly 'normal'. Otherwise, no. Example: 1, 2, 3, 4, 5, 6, 1000 Mean = 145.86 Median = 4

That would provide some evidence that the distribution is symmetric about the mean (or median).

That would provide some evidence that the distribution is symmetric about the mean (or median).

Yes. In the set (9, 10, 11, 12, 13) 11 is the median and the mean.

For the set 3 4 5 8 5, the mean median and mode all have the same value.

The mean is the same as the mode and median.

In a normal distribution the mean, median and mode are all the same value.

Your single number is your only information of the median value of the population, so the median value is the same as your single number. It is also the mode and mean of your sample.

All three increase by that same value.