About Understanding Data

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This page is in progress. There is enough here that you may find it interesting.

Intuitive Meaning

It is always important to grasp the intuitive meaning of data. No measure of exactness, precision, or accuracy means anything without some intuition that it matters.

Qualitative Data

Qualitative data refers not only to the measurement of happiness or motivation. Those sorts of things can be more or less, yet they don’t correspond to a number as well as  masses or distances do – even if someone concocts a happiness “index”.  Qualitative data can also refer to the advantages of a qualitative presentation of what may be perfectly quantitative data. This is so when the sheer amount of quantitative data is very large or the meaning would be overly complex if expressed in quantitative terms.

OnDemand

By marshaling the intuitive powers and using a qualitative presentation, we can have a good data view ondemand: We can see it at a glance. We can answer questions ondemand by just glancing. All we need is to glance at our graph, chart, equation, or pithy sentence.

Information Synonym

Meaning of data as information synonym. The idea here is a bit different than that of word with a similar meaning but rather modes of presentation that show the same data insight is ways which may result in differing shades of meaning.

Key Data Characteristics and Ways to Present Them

Independent Variables or Dependent Variable

Suppose there are two factors that are usually independent – but in a given situation they are dependent. That means that the given situation is somehow creating a relationship that would otherwise not be there.

Increasing or Decreasing

The idea of suggests the presence of more than one variable. For instance, we may be thinking of how the Dow Jones Industrial Average changes from day to day. In that case one variable is the Dow Jones Industrial Average and the other variable is time.

With Respect To (w.r.t.)

We may talk about increasing/decreasing with respect to other dependent variables other than time: For instance, the crime rate may increase when unemployment is higher. In the case that is true, we could say that “the crime rate is increasing with respect to the unemployment rate.” We might say words like “going up as unemployment rises” or “going down as unemployment rises” or “trending up with unemployment” or “trending down with unemployment” as synonyms for “increasing with respect to unemployment” and “decreasing with respect to unemployment”.

Narrative – Graphical – Symbolic – Numerical

Let’s take an example and express the same quantitative observation in all four ways: narrative, graphical, symbolic, and numerical.

Graphical

Decrease is shown in a graph as the graph rising from left to right as illustrated below. Of course, we are mainly seeing trend lines with quite a bit of scatter all about them. While the daily maximum temperature and the daily minimum temperature trend downward with wind speed, the daily difference between the min and max does not appear to trend up nor down with wind speed.

AC_Wind_Temp

Formula

Formulas are powerful because, like a very fine perfume or exclusive skin serum, they are “super-concentrated”: Lot’s of meaning is a small drop. A fancy word for that is semantic density. That semantic density corresponds to the immediate visual recognition we can intuit from the graph. Let’s see why that’s true.

We can look at the graph and see that the blue and orange trend lines appear nearly parallel. Let’s round to a single decimal place and display the two trend line formulas so we can compare them.

y=2.2x+70.3 (Daily Maximum Temperature)

(slope = -2.2)

and

y=2.1x+57.9 (Daily Minimum Temperature)

(slope = -2.1)

We can immediately see looking at the formulas that the slopes are very close.

That both slopes are approximately negative two means that the daily temperature tends on average to be two degrees lower with each increase of one meter per second of wind speed.

It is important to see the dot plots of actual data to remind us that these trend lines and their formulas represent broad trends with wide variation about the trend lines. Let’s

Numerical

The most basic forum of a numerical expression of this data would be too cumbersome to show us anythings. Unlike the dots in the dot plot above, all those rows would not give us a gestalt; that is, it would not form a nice visual.

In order to make a numerical presentation, we might do the following:

Numerical table of wind speed and max temperature.
In this approach we count the number of dots within each range.

See the “68%” in green towards the upper left? What does it mean? It means this: Of all the dots for maximum daily temperature (blue dots), of those with wind speed between 2 and 4, 68% of those have a daily maximum temperature between 70 and 80 degrees Fahrenheit.

 

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