On Mon, 14 Aug 2000, Alexander Bogomolny wrote, inter alia:
> ... If there were alternative definitions, a discussion would be
> interesting. At the time of my first post, I was aware only of a
> single definition that was found in two mathematics dictionaries and
> a statistics book. This is also how I learned it years ago.
> At the time I replied to Dennis Roberts response there still was
> only 1 definition quoted.
Yes, you're quite right; and the definition quoted is in fact correct,
at least as I understand such things. I was countering Dennis' argument
(which was, in essence, that in a histogram the bar widths must be
constant in order that the bar lengths be proportional to relative
frequencies), and remembering (without checking their applicability to
the current discussion) several conflicting definitions of bar charts,
as well as being aware of existing incorrect definitions of histograms.
(RHD, for example, gives
"A graph of a frequency distribution in which rectangles of with bases
on the horizontal axis are given widths equal to the class intervals
and heights equal to the corresponding frequencies."
which errs in two respects: relating heights (rather than areas) to the
frequencies, and specifying "equal" rather than "proportional", although
the latter is arguably but a quibble.)
> For Dennis chose to discuss the merits of Harper's definition.
> Which I thought (and think) was irrelevant.
Yes, I agree: the subject of this thread began as "Histogram for
discrete probability distribution", which is arguably an oxymoron,
since histograms appear to have been conceived orginally with respect
to continuous (or at any rate quasi-continuous) distributions, as
discrete approximations to the graph of a probability density function.
The general problem being discussed by other contributors had to do with
bar charts; for which the Harper Collins definition is incorrect, as a
bar chart is not really a histogram, despite similar outward appearances.
(I suppose one _could_ argue that a histogram is a special kind of bar
chart, one in which the bars are contiguous and the reference axis
continuous, but not that a bar chart is a special kind of histogram.)
> < snip > I may have learned a wrong definition some 30
> years ago and used it since. This may be interesting. But what makes
> a definition right or wrong? I do not know whether the first usage
> and the common usage are always the same. And if they are not,
> what is right or wrong there?
To this question I can only point out that compilers and users of
dictionaries have always operated with some tension between definitions
(and pronunciations) that represent the received wisdom of the ages
(conceived as an immutable ideal) and those that represent the prevalence
of current usage (conceived as changing, if perhaps slowly, over time).
> Also, since you mentioned etymology of the word, here's an item from
> "The Words of Mathematics: An Etymological Dictionary of Mathematical
> Terms Used in English" by Steven Schwatzman. (Follows my signature.)
>
> What do you make out of it? The base width or its variability is not
> mentioned here. Does it mean that Harper Collins is wrong?
No, to answer the last question first. Thank you for the quotation,
it's really interesting. I am not learned in Greek, so I cannot tell
how (or even whether!) to choose between the definition of "histos"
given below ("anything upright," particularly "the upright beam of a
loom," and then, by extension "anything woven, a web, a tissue") and
that offered in RHD ("web (of a loom), tissue"). As nearly all other
English words beginning "histo-" (except for those continuing "-ri-")
refer to tissue, I'm inclined to suspect that "tissue" or "web" is nearer
the root meaning than "upright", especially since the relevant aspect of
a histogram is the area of each rectangle, and the relevant measure of a
tissue or web is its area (a tissue or web being about as close as one
can get to a 2-dimensional, as distinct from 3-dimensional, object).
(And most looms are rectangular, so one could interpret "histogram" as
a kind of visual pun: a series of adjacent rectangles with a common
baseline, like a series of adjacent looms on the weaver's floor.)
> histogram (noun): the second element, -gram, is
> indisputably from Greek gramma "piece of writing,
> picture," from the Indo-European root gerbh- "to
> scratch," because diagrams were originally scratched
> on earth, clay, etc. Reference books explain the first
> element, histo-, in two ways.
> (1) It may be from Greek histos "anything upright,"
> but particularly "the upright beam of a loom," and
> then, by extension "anything woven, a web, a tissue."
> If Greek histos is the source, then the Indo-European
> root is sta- "to stand," as seen in the native English
> cognate stand. According to this explanation, the upright
> bars of a histogram account for its name. (2) Histo- may
> be a contraction of history, from Latin historia, in turn
> from Greek istoria "inquiry, observation." Greek his-tor
> "a learned man," represents a presumed wid-tor, from
> the Indo-European root weid- "to see." Compare the native
> English cognate wise. Etymologically speaking, history is
> "what has been seen (and presumably also understood)."
> According to this explanation, a histogram is a "picture
> history" of a statistical distribution. (3) Whoever coined
> the term histogram may have had both of the above associations
> in mind, since each is plausible. [208, 244, 68]
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