Mean median and mode are always equal?

Answer 1

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.