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Following are the definitions "representative" of the countless articles I have read about data vs information and yet have nothing to say about them. Can anyone just put some accent upon these two so I would better understand statistical science?

Data is a representation of individual facts or statistics in their raw form. Since data contains only figures and numbers, it doesn’t hold any significance until a researcher analyses or contextualizes it. For example, data can signify basic numbers regarding the price of an object, the score on a test, or the current temperature outdoors. Information is an interpretation of data, where researchers identify patterns and draw conclusions based on raw figures. Using data, a researcher can draw meaningful conclusions about their desired subject. Information also has different meanings based on the context. For instance, the data tells you the temperature outdoors. One person may conclude that the temperature is high, while another person declares that it's low. When someone describes the temperate as being high, they’re providing information about their interpretation of the weather.

One more example that I found: Analysts conduct market research that entails data and information. Suppose they track the amount of money consumers between the age of 18 and 24 spent on hair products in 2018, representing data. The information includes a comparison of that figure to previous years and explanations of why it changed. Within the marketing industry, figures and interpretations enable professionals to monitor trends in consumer buying behaviors and how products perform on the market.

What is data, and what is information in this spreadsheet?
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    $\begingroup$ Whenever words are used both generally and technically (here, within statistical science) it is common to find that definitions outside statistics can be unhelpful or misleading and that different groups don't necessarily use terms consistently. In statistical practice, data are what you have in a dataset, and that's not quite circular. Thus in the example, identifiers and part names are to many of us data too. $\endgroup$
    – Nick Cox
    Jun 11 at 9:42
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    $\begingroup$ In statistical practice, setting aside the specific sense of information theory, I often see or hear people mentioning information, but in a loose informal sense of whatever can be found that is interesting or useful. What information is to be found in the data that helps a researcher or a client? I love dictionaries, but definitions follow common usage; they don't determine correct usage in any sense stronger than a recommendation. (I wish the politicians and the pundits would give us back the original meaning of parameters, for example, but that is a futile wish.) $\endgroup$
    – Nick Cox
    Jun 11 at 9:44
  • $\begingroup$ @NickCox Sir, I just read an article where the blogger defines information in a raw sense. And, I quote, "Information is data + meaning." That makes me more confused. Sth to say on this? $\endgroup$
    – Vinay Sharma
    Jun 11 at 10:26
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    $\begingroup$ It's the same question. The blogger seems to agree with me (and more importantly who would ever disagree?) in wanting to identify meaning within data. I wouldn't want to use their wording or style -- which is pseudo-mathematical to my taste, but that could be seen as pedantry too -- yet I agree very broadly with what I take to be their implication. The meaning is wrapped up in the data, however, not separate from it, so addition makes no strict sense. I can't say more from the little you cite, with no reference. $\endgroup$
    – Nick Cox
    Jun 11 at 10:55
  • $\begingroup$ There is some overlap in the answers here, which is mostly fruitful. I still prefer my own comments, made early in the thread, so I have recycled them into yet another answer. $\endgroup$
    – Nick Cox
    Sep 5 at 8:55

6 Answers 6

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TL;DR when you make some observations and record them (using whatever means) the recordings are data. What the data represents, encodes, or communicates, is information.

This is nicely explained by Wikipedia

Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level, information pertains to the interpretation (perhaps formally) of that which may be sensed, or their abstractions. Any natural process that is not completely random and any observable pattern in any medium can be said to convey some amount of information. [...]
Information is often processed iteratively: Data available at one step are processed into information to be interpreted and processed at the next step. [...]

As noticed by Peter Flom in his answer, "information" is not a term that you would commonly see used in statistics. You would see it used in statistics in the context of information theory. Information theory was invented by Claude Shannon and others in the first half of the XX century and is

the mathematical study of the quantification, storage, and communication of information.

Information may be communicated so that a message sent between the communicating parties contains some amount of information, whereas different messages can contain different amounts of information. In Chinese languages, you may use a single character to describe some concept, while to encode the same information in English, you would need to use multiple characters. Information can be stored, sometimes we may compress the data, where an efficient compression algorithm would enable you to store a large quantity of information within a small space. Finally, in statistics, information may be encoded using a statistical model so that the model carries it with as little loss of information as possible.

As you can see, this is an academic discussion of abstract concepts. It does not really apply to using Excel software unless you are interested in a philosophical discussion on how it processes data while the information is the knowledge and facts we interpret from the data. As the saying by Alfred Korzybski goes, "A map is not the territory". As for statistical science, again if you are interested in theoretical considerations, information theory has its implications. The concepts of information and entropy inspired some statistical methods and tools (maximum entropy, K-L divergence, etc).

For a more formal and in-depth discussion, see Stanford’s Encyclopedia of Philosophy entry on “information”.

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  • $\begingroup$ I hope there’s a simple way to define these terms. Defining information as something that has the power to inform is synonymous to define a carbonator engine as an engine where a carbonator is used. It doesn't add up. I usually think when we define sth generally, we create layers upon it, which conceals the specialness, uniqueness of that term. I don't mean to be blunt. $\endgroup$
    – Vinay Sharma
    Jun 10 at 19:24
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    $\begingroup$ @VinaySharma if you read the answer carefully, information is defined through examples. It is whatever is communicated, encoded, contained, etc (depending on context). $\endgroup$
    – Tim ♦
    Jun 10 at 20:32
  • $\begingroup$ I add some other material to my post, see if you can help. $\endgroup$
    – Vinay Sharma
    Jun 11 at 2:47
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    $\begingroup$ @VinaySharma I haven't said anything like this and don't understand your comment. $\endgroup$
    – Tim ♦
    Jun 12 at 4:32
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    $\begingroup$ +1 for your wonderful answer. Just came to this question to comment something similar to what you say after reading the preface of the book "High-Dimensional Data Analysis with Low-Dimensional Models: Principles, Computation, and Applications". Much recommended to anyone interested in these topics! $\endgroup$
    – Amelian
    Jun 22 at 2:41
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Welcome to the site and I can certainly see why those passages confuse you; they confuse me, too. I had always thought of the two terms as pretty much synonymous.

So, I pulled out the Oxford Dictionary of Statistics by Upton and Cook and looked up "Data" and it says

information, usually numerical or categorical.

For "information" it just says "see Fisher's Information" which is not what you are talking about here.

I don't have access to the Encyclopedia of Statistics (I bet other people here may have access) but Encyclopedia Britannica is not behind a paywall. Its article on statistics is useful In part, it says:

Data are the facts and figures that are collected, analyzed, and summarized for presentation and interpretation.

The Cambridge Dictionary of Statistics by Everitt and Skrondal is also available online. Their entry for "data" sends you to "data set" which says:

A general term for observations and measurements collected during any type of scientific investigation.

It does not have an entry for "information".

Now, back to my own thoughts. Statistics uses many terms that are in general use, but uses them in its own specialized ways. (Power, significance, censoring, confidence .... the list is long). "Information" in statistical use has a specialized meaning. Don't use it as a general term.

The passages you quote are more philosophical. Like a lot of philosophy, they are interesting and confusing. But I don't think they are relevant to understanding statistics (you also ask about understanding Excel, but ... I don't know what that has to do with this).

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    $\begingroup$ Well, don't mind though nothing is answered, just more philosophy. $\endgroup$
    – Vinay Sharma
    Jun 10 at 19:10
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    $\begingroup$ @VinaySharma you asked a question about definitions of abstract concepts. The answer to such a question cannot be non-philosophical. $\endgroup$
    – Tim ♦
    Jun 11 at 6:07
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    $\begingroup$ What wasn't answered? $\endgroup$
    – Peter Flom
    Jun 11 at 11:11
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A datum is a single measurement of a thing. Information is something that gives you knowledge about a measurement that you didn't even make. For example, you can wake up in the morning, and see the sun rising, and this observation is a datum - you actually literally saw the sun rise. After years of seeing the sun rise in the morning, you can plan tomorrow "I'm going to wake up tomorrow and watch the sunrise" - How do you know that you will be able to make such a measurement tomorrow, of the sun rising? This ability to expect a certain measurement without actually taking it is "information". We generally also call the additional knowledge that we gain when we actually wake up tomorrow and see that the sun did, in fact, rise "information" as well, because the actual observation also informs us about what the observation "could be".

tl;dr; information is about what a datum "could be"

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  • $\begingroup$ So, how your explanation fits specifically in the following examples I cite from a web page, can you help me understand these examples? Suppose I track the amount of money consumers between the age of 18 and 24 spent on hair products in 2018, representing data. The information includes a comparison of that figure to previous years and explanations of why it changed. $\endgroup$
    – Vinay Sharma
    Jun 10 at 19:31
  • $\begingroup$ The data tells you the temperature outdoors. One person may conclude that the temperature is high, while another person declares that it's low. When someone describes the temperate as being high, they’re providing information about their interpretation of the weather. Can you explain this as well according to your definition? $\endgroup$
    – Vinay Sharma
    Jun 10 at 19:32
  • $\begingroup$ But, but, but, what is the difference between "information" and "knowledge"? $\endgroup$
    – Stef
    Jun 12 at 13:35
  • $\begingroup$ @Stef language can only convey so much, and definitions must fall back on a primitive notiion (which, IMHO, depend on experience) at some point, lest they fall into an infinite regress. I am happy to help define terms in context of something that you stipulate that you already know, but bootstrapping knowledge from language and nothing is not possible. $\endgroup$
    – Him
    Jun 12 at 14:08
  • $\begingroup$ @Stef if you are genuinely interested in clarifications, then some combination of Bayesian notions of "uninformative priors" and Shannon's theory of entropy as information are the roots of the informal description I have here. For a coin, from square one, we can adopt a uniform prior because it provides the least information, in the Shannon sense, about each future datum - the actual measurements. $\endgroup$
    – Him
    Jun 12 at 14:15
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Like many people, I use Strava to record my bicycling activity.
Every second it records my latitude, longitude, and elevation:

lat="43.4458280" lon="-80.5437870"> <ele>351.9</ele> <time>2023-06-10T18:31:30Z</time>
lat="43.4458420" lon="-80.5437720"> <ele>351.8</ele> <time>2023-06-10T18:31:31Z</time>
lat="43.4458590" lon="-80.5437620"> <ele>351.8</ele> <time>2023-06-10T18:31:32Z</time>

A three hour trip can produce over 10,000 data points.
There's too much of it, yet looking at small parts of it is mostly useless.
That is data.

The application also plots these locations on a map and calculates a graph, based on this data, showing how fast I was moving at any specific time or place. It also plots a profile of the elevation over time, providing a visual presentation of the height, length, and steepness of all the hills on the trip. In addition, the software provides a dynamic visual link between each position on the map, the elevation profile, and the speed graph.
That is information.

Briefly, from a human-centric point of view, I would characterize data as a large collection of facts that are individually useless, and information as a smaller collection of immediately useful facts that can be derived from that data.

To specifically answer "What is data, and what is information in this spreadsheet?": each individual line is a piece of data, and that if the table included a "Total" line at the end, that line would be information.

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    $\begingroup$ Could you provide definintions as well as examples? I guess, most peopke would say that what yoy call “information” are are data vidualizations and statistics. $\endgroup$
    – Tim ♦
    Jun 12 at 5:01
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    $\begingroup$ Data and more data $\endgroup$
    – Stef
    Jun 12 at 13:37
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Whenever words are used both generally and technically (here, within statistical science) it is common to find that definitions outside statistics can be unhelpful or misleading and that different groups don't necessarily use terms consistently. In statistical practice, data are what you have in a dataset, and that's not quite circular. A dataset is in practice what you hold in your software. Thus in the example, identifiers and part names are to many of us data too.

In statistical practice, setting aside the specific sense of information theory, I often see or hear people mentioning information, but in a loose informal sense: information is whatever can be found or inferred that is interesting or useful. What information is to be found in the data that helps a researcher or a client? What do the data mean or imply to the analyst and whoever uses their results?

I love dictionaries, but definitions follow common usage; they don't determine correct usage in any sense stronger than a recommendation. (I wish the politicians and the pundits would give us back the original meaning of parameters, for example, but that is a futile wish.)

The OP added a comment (here edited slightly)

I just read an article where the blogger defines information in a raw sense. And, I quote, "Information is data + meaning." That makes me more confused. Something to say on this?

I see this as the same question. The blogger seems to agree with me (and more importantly who would ever disagree?) in wanting to identify meaning within data. I wouldn't want to use their wording or style -- which is pseudo-mathematical to my taste, but that could be seen as pedantry too -- yet I agree very broadly with what I take to be their implication. The meaning is wrapped up in the data, however, not separate from it, so addition makes no strict sense. I can't say more from the little you cite, with no reference.

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  • $\begingroup$ Anything from Nick can rarely be questioned. $\endgroup$
    – Vinay Sharma
    Oct 3 at 20:35
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Wikipedia might not be the most authoritative source, but I find its definition pretty clear:

In common usage and statistics, data (US: /ˈdætə/; UK: /ˈdeɪtə/) is a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally.

That has also been pretty much my understanding even before having read it.

So, applied to your table, it only contains data. You might analyse the data and discover that the frequency of the digit '5' in the 'Price' column rises as the part number increases. That would be 'information'.

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