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The mean, median, and mode are not always equal.

For example, consider the set of 5 values {2, 3, 5, 10, 10}.

The arithmetic mean is 6. (The values sum to 30, and 30 divided by 5 is 6.)

The median is 5. (The middle number of the 5 values, when sorted, is 5.)

The mode is 10. (The value 10 appears most often in the set.)

And, you probably didn't ask, but:

The geometric mean is the fifth root of 3000, or about 4.96.

The harmonic mean is 150 divided by 37, or about 4.05.

The quadratic mean is the square root of 47.6, or about 6.9.

Although the word "average" can technically be used to describe all of these values, in common parlance the word "average" refers to just the arithmetic mean.

Q: Mean median and mode are always equal?

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who discovered mean median and mode

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

a single number, -3, is its own mean, median, and mode.

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.

If the distribution is positively skewed , then the mean will always be the highest estimate of central tendency and the mode will always be the lowest estimate of central tendency (If it is a uni-modal distribution). If the distribution is negatively skewed then mean will always be the lowest estimate of central tendency and the mode will be the highest estimate of central tendency. In both positive and negative skewed distribution the median will always be between the mean and the mode. If a distribution is less symmetrical and more skewed, you are better of using the median over the mean.

Related questions

the median and mode are but the mean is not

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

The median and mode.

mean, median and mode

100,100,100,100,100,100

The mean is the same as the mode and median.

who discovered mean median and mode

All equal.

The mean, median, and mode of a normal distribution are equal; in this case, 22. The standard deviation has no bearing on this question.

There are may situations. For example, the mean , median and mode for the set {1,2,5,5,5,6,11} are all 5. But the data are not symmetric or have any other special characteristic.

The median is 9 and the mode is 18 and the mean is 11

Yes, mode equals median in a normal distribution.