No, Average is any measure of central tendency, which include all of the median, mode, and the various means (harmonic, geometric, arithmetic,...), as well as some others.
The mode is the most broadly applicable, since (at least if you accept multiple values) it is well-defined on any, even merely categorical, data. The median requires ordinal data, and the various means tend to require at least interval-level measures (some of them require ratio-level measures.)
The arithmetic mean seems to be the most common grade school mathematics “average”, possibly because its the one that does the most to exercise basic arithmetic skills. But its rarely, when distinct from the median and mode, the most useful, and often doesn’t match the intuitive understanding of “average”.
> Incorrect, median, mean, and mode are all types of averages.
There's a bunch of means (arithmetic, geometric, and harmonic, for instance), and they are all (as well as median and mode) averages.
Though, usually when people say "mean" without further specifics they mean the "arithmetic mean", and usually when they say "average" without further specifics they also mean "arithmetic mean" (though "median" is also fairly common, and "mode" isn't that uncommon.)
> you'd think a math teacher of all people would know not to use "average" when they really mean "median".
I think a math teacher would be well aware that "average" can be used for "median", "mode", "arithmetic mean", or any of the other means (geometric, harmonic, etc.), as well as other computed values that are somewhere in the space bounded by the extremes of a data set, and would likewise be aware that, while in a formal context "average" should -- for that reason -- be avoided in favor of identifying the specific measure more precisely, it was acceptable and unambiguous to use "average" for any of those, including the median, where context made it clear which was intended.
> I've heard of the median and mode being associated closely with the "average," but never as a synonym.
They aren't synonyms, they are more specific terms.
In colloquial language, an average is a single number taken as representative of a list of numbers. Different concepts of average are used in different contexts. Often "average" refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged. In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage any of these might be called an average value.
"Average" is a colloquial term referring to any measure of central tendency. The arithmetic mean is just the most common kind of average, not the only kind.
Incorrect, median, mean, and mode are all types of averages. Usually when people say average they mean the mean, but they're all different kinds of averages trying to identify the central tendency.
"Average: a number expressing the central or typical value in a set of data, in particular the mode, median, or (most commonly) the mean, which is calculated by dividing the sum of the values in the set by their number." -- Google
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.
Median is an average. There are typically three averages in common use; mode, median and (arithmetic) mean. That people generally use "average" as short for "(arithmetic) mean average" is a colloquial shorthand.
Median is an average, just like the mode, arithmetic mean, geometric mean, harmonic mean, etc., are, even though most of the time when “average” is used without specifying which one, its actually the arithmetic mean.
I know people learn this in middle school, but I've never seen an actual scholarly work call the median or mode "the average"--and I think I'd find it slightly misleading if they did.
"Typical", "likely", (etc) are all fine, but to me, "average" strongly implies "mean."
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]
> Reporters and editors still equating average and median.
Median is an average and usually the most relevant average, in the cases where you don't have a distribution where the main averages (median, arithmetic mean, and mode) are all the same.
"Different concepts of average are used in different contexts. Often "average" refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged. In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage any of these might be called an average value."
No, Average is any measure of central tendency, which include all of the median, mode, and the various means (harmonic, geometric, arithmetic,...), as well as some others.
The mode is the most broadly applicable, since (at least if you accept multiple values) it is well-defined on any, even merely categorical, data. The median requires ordinal data, and the various means tend to require at least interval-level measures (some of them require ratio-level measures.)
The arithmetic mean seems to be the most common grade school mathematics “average”, possibly because its the one that does the most to exercise basic arithmetic skills. But its rarely, when distinct from the median and mode, the most useful, and often doesn’t match the intuitive understanding of “average”.
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