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Univariate Statistics: Tests & Examples

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Instructor: Jessica McCallister

Jessica has a Doctorate degree in Social Work

Univariate statistics is the field of statistics that allows the researcher to describe individual variables. Learn about the basic statistical test which include mean, mode, median, standard deviation, variance, and range along with examples. Updated: 09/13/2021

What are Univariate Statistics?

The field of univarite statistics focuses on one variable at a time and does not involve any testing of variables against each other. Rather, it provides an opportunity for the researcher to describe individual variables. Thus, this category of statistics is also referred to as descriptive statistics. In this lesson, we will discuss some basic statistical tests under this category including mean, mode, median, standard deviation, variance and range.

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  • 0:02 What are Univariate…
  • 0:36 Mean & Mode
  • 1:46 Median
  • 3:01 Standard Deviation & Variance
  • 4:40 Range
  • 5:11 Lesson Summary
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Mean & Mode

Let's say you were working as a psychologist and had 10 clients in your caseload. You might want to know what the average age of your client group is. In order to do this, you would add up their ages and then divide by the total number of clients to find their average age. By learning their average age, you are locating the mean, which is the same thing as the mathematical average. For example, let's consider we have 10 clients with the ages shown here:

Client #1 = 32 years old

Client #2 = 45 years old

Client #3 = 20 years old

Client #4 = 33 years old

Client #5 = 50 years old

Client #6 = 44 years old

Client #7 = 40 years old

Client #8 = 28 years old

Client #9 = 29 years old

Client #10 = 48 years old

When you divide the total of 369 by 10 clients, the mean age across all clients is 36.9 years old.

Another univariate statistic used in psychology is the mode, which simply means the most reported number. If you are wanting to know the most reported age across your clients from the list of ages from the previous example, you would see that there is no mode because everyone's age is different, and there is no one age that is reported more than any other age, or more than once, for that matter. If there was a client age that was reported more than once, then you would have a modal age.

Median

The third test, the median, is calculated a bit differently than the mean. The median is when half the group's age falls below the middle value, and the other half of the group's age rests above the middle value. You can locate the median, or middle, value for any information that is presented in numerical format. In order to find the median value, the following statistical process must be used:

  • Line up all ages from smallest to largest
  • If the total of the set of numbers is even, then add up the middle two numbers and divide by 2
  • If the total of the set of numbers is odd, then the middle number is the median.

For example, if you lined up all the clients' ages in order, your list would look like this:

Client #3 = 20 years old

Client #8 = 28 years old

Client #9 = 29 years old

Client #1 = 32 years old

Client #4 = 33 years old

Client #7 = 40 years old

Client #6 = 44 years old

Client #2 = 45 years old

Client #10 = 48 years old

Client #5 = 50 years old

Then you would take the middle two values, 33 and 40 years old, add them up, and then divide by 2 to find the median to get the median age of 36.5 years old.

Remember, the median represents the middle value, so that half of the group is below the middle value and half the group is above the middle value. Don't confuse the mean with the median or think they are the same just because they may come out to similar values! They provide different statistical purposes.

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