We can classify data into 1 of 4 levels of measurement. These
levels of measurement will be important, because certain calculations
can be done with only certain kinds of data. How's that for vague?
The first (and weakest) level of data is called nominal
level data. Nominal level data is made up of values that
are distinguished by name only. There is no standard ordering
scheme to this data.
Ex. The colors of M&M candies is an example of nominal level
data. This data is distinguished by name only. There is no agreed
upon ordering of this data, although we each may have an opinion
about which should be listed first. I'm partial to brown and may
feel that brown should always be listed first, but you may like
green and feel it should go first.
The second level of data is called ordinal level data.
Ordinal level data is similar to nominal level data in
that the data is distinguished by name, but it is different than
nominal level data because there is an ordering scheme.
Ex. Movies on a certain TV show are classified as 2 thumbs up,
1 thumb up, or 0 thumbs up. There is an order here. A movie that
receives 2 thumbs up is better that a movie that receives 1 thumb
up (supposedly anyway). How much better is a movie that receives
2 thumbs up than a movie that receives 1 thumb up? Is it 1 thumb
better? What exactly does that mean?
Ex. Voters are classified as low-income, middle-income, or high-income.
This is an example of ordinal level data. We do know that people
in the low-income bracket earn less than the people in the middle-income
bracket, who in turn earn less than the people in the high-income
bracket. So there is an ordering scheme to this data.
The thing that ordinal level data lacks is that you can't measure
the difference between two pieces of data. We know that high-income
people earn more than low-income people, but how much more. This
is where the third level of data comes in. Interval level
data is similar to ordinal level data in that it has a definite
ordering scheme, but it is different in the fact the differences
between data is meaningful and can be measured.
Ex. The boiling temperatures of different liquids are listed.
This is an example of interval level data. We can tell whether
a temperature is higher or lower than another, so we can put them
in an order. Also, if water boils at 212 degrees and another liquid
boils at 284 degrees, the second temperature is 72 degrees higher
than the first. So the differences between data are measurable
The one thing that interval data lacks is a zero starting point.
Is 0 degrees the absolute lowest temperature? As anyone from Hibbing,
Minnesota will tell you, temperatures go below 0 degrees on a
regular basis. Because there is no zero starting point, ratios
between 2 data values are meaningless. Is 75 degrees three times
as hot as 25 degrees? No, because the ratio of 75 to 25 (i.e.
3 to 1) is meaningless here. Think about the following cooking
Ex. A brownie recipe calls for the brownies to be cooked at 400
degrees for 30 minutes. Would the results be the same if you cooked
them at 200 degrees for 60 minutes? How about at 800 degrees for
15 minutes? I think we would get 3 different types of brownies
: just right, awful gooey, and awful crunchy. The problem is that
200 degrees is not half as hot as 400 degrees, and 800 degrees
is not twice as hot as 400 degrees.
This is where Ratio level data comes in. Ratio level
data is just like interval level data, except that ratios make
sense. I guess it's pretty well named.
Ex. Four people are randomly selected and asked how much money they have with them. Here are the results : $21, $50, $65, and $300.
Is there an order to this data? Yes, $21 < $50 < $65 < $300.
Are the differences between the data values meaningful? Sure, the person who has $50 has $29 more than the person with $21.
Can we calculate ratios based on this data? Yes because $0 is
the absolute minimum amount of money a person could have with
them. The person with $300 has 6 times as much as the person with
Other examples of ratio level data would be ages of people, scores
on exams (graded from 0 to 100), and hours of study for a test.
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