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Comment by p1necone | Hacker News Reader

I was taught in school that average can refer to mean, median or mode (is that common everywhere?). Mean seems to be the default when not specified but journalists really should be specific (also as you point out, median is more often than not the best/least misleading one to use).

Edit: wikipedia (https://en.wikipedia.org/wiki/Average) seems to suggest that they can all be considered "averages".

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I disagree with the assertion (it is unsourced on wikipedia) -- colloquially the average is the arithmetic average, not a median or mode. At a next level up, average typically refers to

- Arithmetic mean

- Geometric mean (exp of average of log values)

- Harmonic mean

Mode and medians are measures of centrality, true, but are not equivalent to the arithmetic mean.

Fun fact (h/t John Myles White) the arithmetic mean, median, and mode are the same calculation under different L-p norms.[0]

[0] http://www.johnmyleswhite.com/notebook/2013/03/22/modes-medi...

I was a math major and was taught (as in elementary, middle, and high school), that the "average" is the mean...

I agree. Personally, I was never taught that they were all synonymous. For whatever it's worth, I was a EE major.

I think it would be very unusual to refer to the mode as the average, especially if it wasn't close to the median or mean.

I think most people would agree, making it the average belief (by mode!)

Mode is the most common meaning for "average" in vernacular English. When someone says "I'm just your average guy," they are not doing math. They're comparing themselves to what the majority (or perceived majority, i.e. plurality) of other people are like.

or perhaps implicit in the language of "I'm just your average guy" is that the central limit theorem applies.

I assume they are intentionally conflating median and mean to elicit a more emotional response since they specifically mentioned median and omitted mean.

Whoa that's wrong. Average == mean. Always. In Excel, in NumPy, the average() function calculates mean.

No, it's not. Average can mean mean (any of them: e.g., geometric or harmonic as well as arithmetic), median, or mode.

Usually, people using “average” outside of a specialized context where some other average is the conventional default mean arithmetic mean, but that's not the only thing it can mean, and, frankly, it's better just to avoid using “average” to refer to any summary statistic and just use the specific name for the statistic you want to use.

You are 100% incorrect. Go look it up in the dictionary.

Mean == Average, by definition. Median is the middle point of a set, and mode is completely different, it's the most frequent number in a set. In no shape of form is "mode" ever confused with "average".

The first few dictionaries I looked at online said, in the first or second definition for “average”, something about it being “mean, median, or mode”:

https://www.merriam-webster.com/dictionary/average https://en.oxforddictionaries.com/definition/average https://en.m.wiktionary.org/wiki/average

I agree that arithmetic mean is usually what’s meant, but clearly median and mode can also be rightfully called “averages”.

I like Merriam-Webster's first definition, which eschews any math terms and defines it as the value most representative of a set of data

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