# Psychology Statistical Data: Shapes & Distributions

Instructor: Emily Cummins
How do we visualize data? In this lesson, we'll talk about distributions, which are visible representations of psychological data. We'll talk about the major kinds of distributions that we generally see in psychological research.

## Psychology and Data

What do you visualize when you think about the word 'data?' You probably think about numbers, or graphs, or maybe even mathematical equations. When psychologists collect data they have particular ways of representing it visually. This visualization, whether it's a graph or a table, helps us interpret our data. This is known as a distribution and it's just what it sounds like: how is data distributed in some kind of pattern?

In this lesson, we'll go over the kinds of distribution that we generally see in psychological research.

## Frequency Distribution

There are few types of distributions but before we talk about specific shapes that data take, we need to talk about the difference between a frequency distribution and a probability distribution. A frequency distribution is simply the visual display of some data. Let's say you interview 30 people about their favorite jelly bean flavor. Maybe 10 people say orange, 5 people say red, 8 people say purple, and 7 people say green. You could put this information in a graph and it will have some sort of shape, but it only tells us something about these 30 people.

What if you want to know how likely it is that all jelly bean eaters out there prefer orange? In this case, you'd need a probability distribution. A probability distributions tell us how likely an event is to occur in the real world. Since we can't really ask every single person out there who eats jelly beans what his or her favorite flavor is, we need a model of that. Statisticians can calculate this using equations that model probabilities. When statistical calculations are involved, it's a probability distribution.

## Normal Distribution

The most common type of distribution is a normal distribution. This means that the distribution of this data is symmetric and, in fact, is bell-shaped. This is why the normal distribution is also called the bell curve. Take a look at the graph below:

Often times, when a researcher collects data it falls into a general, or normal, pattern. Than means we can expect to see this kind of pattern for a lot of different data. IQ scores and standardized test scores are great examples of a normal distribution.

The normal distribution is really important in statistics and a major reason why has to do with what is known as the central limit theorem. This theorem basically states that the distribution (remember, this basically just means the shape of the data) of any large enough sample of variables will be approximately normal.

So, if you are looking at the average height of females, the average grade point of high school students, or the median income of people aged 24-34, if you have a large enough sample from which you collected data, you're going to get a normal distribution.

In psychology, the normal distribution is the most important distribution and a normal distribution is a probability distribution.

## Skewed Distributions

What about when data doesn't look like a bell when you graphically display it? Some distributions might be skewed, meaning they are asymmetrical, unlike our symmetrical bell curve described above.

Let's say a teacher gives a pop quiz but almost no one in the class did the assigned reading the night before and many students do poorly. When the teacher computes the grades, he will end up with a positively skewed distribution.

If, on the other hand, someone in the class found out about the pop quiz before hand and many more people in the class did the readings than normal, the scores will be unusually high. This will result in a negative skew.

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