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Welcome to the Department of Science and Mathematics at Montclair State University!

STATISTICAL CONSULTING PROGRAM

The goal of this website is to provide you with many useful  facts on various kinds of DATA TYPES known in statistics.

Here are four major data types whose more detailed descriptions can be found below:

Quantitative

Discrete

Continuous

Categorical

The descriptions are provided below.  You will see that the data types are described in the same order as you see them listed above---starting with the quantitative and ending with the categorical data type.

•   Quantitative Data
Quantitative data (metric or continuous) is often referred to as the measurable data. This type of data allows statisticians to perform various arithmetic operations, such as addition and multiplication, to find parameters of a population like mean or variance. The observations represent counts or measurements, and thus all values are numerical.  Each observation represents a characteristic of the individuals in a population or a sample.

Example: A set containing annual salaries of all your family members,  measured to the nearest thousand, contains quantitative data.  Take, for instance, family X.  Here is a possible data set for this family: mother \$25,000, father \$30,000, myself \$35,000, my wife \$32,000, uncle Joe \$20,000, etc.

• Discrete Data
According to the New World Dictionary of the American Language, the definition of "discrete" is the following: separate and distinct; not attached to others; unrelated; made up of distinct parts;       discontinuous.
Statistically speaking, discrete data result from either a finite or a countable infinity of possible options for the values present in a given discrete data set.  The values of this data type can constitute a sequence of isolated or separated points on the real number line. Each observation of this data type can therefore take on a value from a discrete list of options.

The discrete data type usually represents a count of something.  Some examples of this type include the number of cars per family, a student's height, the number of times a person yawns during a day, a number of defective light bulbs on a production line, and a number of tosses of a coin before a head appears (which process could be infinite in length).

Here are three kinds of discrete data:

• 1. Discrete numerical data is discrete data that consists of numerical  measurements  or counts.  A set that consists of discrete numerical data contains numbers. It is all quantitative data, which allows us to find population or sample parameters like mean, variance, and others.  Discrete numerical data sets do not always consist of whole-numbers (or integers), but they may also take on the values of fractions and decimals.
Example: A set containing the heights of students in your high school graduating class, rounded to the nearest inch, represents such data type.  It is very important to remember here to round the numbers up.  If we do not, and we accept measurements such as 62.896 in., 63.277... in., 67.8435... in., we will be dealing with continuous data type, described below.   With discrete data type, there is a countable number of observations involved.  For example, a set containing possible students' heights will consist of integers starting at 0 in and ending at perhaps 84 in, unless there are students over 7 feet tall, which is highly unlikely. Integers are countable and that is what makes this set discrete.

Also, a number of Farmland Dairies ultra-pasteurized whole milk bottles in different stores can result in values like 0, or 1, or 2, or 3, and so on, and that would also be considered discrete numerical data. We can count all possible values. Scroll down for a variation to this example used to describe the continuous data type.

• 2. Discrete ordinal datais discrete data that may be arranged in some order or succession, but differences between  values  either cannot be determined or are meaningless.    There are only relative comparisons made about the differences between the ordinal levels.
Example: Consider the following statement: "In a group of twenty workers, five are "best," ten are "good," and five "need improvement."  Although there are obvious differences between each category (best, good, and need improvement), and we can arrange them in order of worse to best or vice versa, there is not much more we can do to compare them.  We do not know how much better is "best" from "good" or "good" from "need improvement." In this case, we could have also used numbers instead of words, ex. 1 for best, 2 for good, and 3 for need improvement, and the data type would still be ordinal.  The numbers still lack any computational significance.
• 3. Discrete qualitative (nominal) data is discrete data that cannot be arranged in any order. It can be represented by numbers, letters, words, and other forms of notation or symbolism, but there are no ranking differences to be determined.  Each category or group will certainly be different from the others, but it will be equally significant.  This data type will only consist of names, labels, or categories.
Example: Gender, political parties, or religions are just some of many qualitative sets that exist around us.  Take, for example, these statements: 1. "In a group of twenty workers, there are ten women and ten men," or 2. "In a group of twenty workers, there are five Republicans and four Democrats, and 1 Independent." The categories such as women and men, or republicans,  democrats, and independents, can be talked about, described, and even criticized, but not officially ranked.  There are no accepted schemes to put these categories in any meaningful order.

• Continuous Data
According to the New World Dictionary of the American Language, the definition of "continuous" is the following:               going on or extending without interruption or break; unbroken; connected; points whose value at each point is      approached by its values at neighboring points.

Continuous quantitative data result from infinitely many possible values that the observations in a set can take on.  The term "infinitely," however, does not refer to the "countable" term we have seen with discrete data types.   Continuous data types involve the uncountable or non-denumerable kind of infinity, which is frequently referred to as the number of points on a number line (or an interval on a number line). In other words, the observations of this data type can be associated with points on a number line, where any observation can take on any real-number value within a certain range or interval.

Example: Temperature readings are one example of such data set.  Each reading can take on any real number value on a thermometer.  If we agree that during a particular day the temperatures between 10am and 6pm will be somewhere between 32 and 100 degrees Fahrenheit, the truth is that these temperatures could take on any value in that range.  For example, consider the following possible temperature readings given in degrees Fahrenheit: 90.333..., 75.324, 40.23..., 85, or 65 multiplied by Pi (or 65 multiplied by 3.1415...).

Another example will be a different approach to the Farmland Dairies ultra-pasteurized whole milk bottle example used with a description of the discrete numerical data.  If, instead of measuring the number of bottles in different stores, we measure the amount of milk in each one half gallon bottle in different stores, those values could, for instance, be 0.498 gallon, or 0.5025 gallon, or any value in between.  The observed values will be represented by real-line values, and there is an uncountable number of possibilities for that to occur.

• Categorical Data
Categorical data, also called qualitative or nominal, result from placing individuals into groups or categories.   The values of a  categorical variable are labels for the categories. We have described both ordinal and qualitative categorical data types above.

1. Discrete ordinal data --described above

2. Discrete qualitative data--described above

Should you have a comment or would like to contact us for statistical consulting, you may e-mail us at scp@stat.montclair.edu
or go to our  SCP main page.

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