The Importance of Descriptive Statistics

Hello. My name is Dominic Dwyer.

I'm a professor in the school of psychology at Cardiff University.

And in this course I'll be talking about descriptive statistics.

Although my own research is more about animal learning and behaviour,

it happens that statistics is the topic that I have lectured

on for the longest period of time in my career.

This course is about descriptive statistics,

and in this first lecture,

I want to give a bit of background as to why we need descriptive statistics.

And the need is simple.

Psychologists create vast amounts of data.

Even a simple experiment might involve making observations on

a dozen set of people and dozens of times.

Even in that case,

the set of numbers created. The measurements

is so large that it's almost impossible to get an impression

of what it means or looks like

without some sort of compression without putting things together.

And that is where descriptive statistics come in.

Essentially,

descriptive statistics are summary features.

There are a limited set

of numbers that represent the whole of the data that's being talked about,

often

their combined with things like graphics or

tables to present these summary statistics.

So essentially

with descriptive statistics were taking a very

large amount of data and compressing it in

a way that allows us to get a handle on what that whole data means

in average, on average, as it were.

And there are two key things about descriptive statistics.

One of them is the central tendency.

Essentially, the central tendency is asking about what data is most typical.

Where do the scores cluster together?

In a sense, what is the data like on average?

The other key thing is dispersion.

How spread out the data is

essentially, It's a question of saying, Well, how typical

is the typical?

If you have

a very large dispersion,

then your measure of central tendency

isn't a great reflection of the data set as a whole.

However,

if you have a small amount of dispersion or spread,

then actually

the central tendency

is a good reflection of the data set as a whole.

No,

I've talked so far about the concepts of central tendency,

the typical or

average set of scores

and range or dispersion

as generalities.

What about specifics?

Well,

technically speaking,

in mathematical terms,

the word average refers to any measure of central tendency,

but

the three averages or measures of central

tendency were most interested in this course.

Are the arithmetic mean, which in common parlance, is the average

the median or middle score of a set of data when it's

re ordered from lowest to highest

and the mod

the most common score

in terms of dispersion?

Then

we're interested in the standard deviation,

which is a measure of dispersion, or spread

that is mainly associated with the mean as a measure of central tendency.

Then there's the range,

which is the difference between the top and bottom scores

or,

in some cases, something like the inter quartile range,

which is a concept I'll have a little bit to say about later.

So

that's the overview measures of descriptive statistics we use in order

to compress large amounts of data into a manageable fall.

We often present them using graphs and tables,

and the two things we want to use

in terms of descriptive statistics

is some measure of central tendency, or average, like the mean the median or the mode

and some measure of variability or spread

like the standard deviation or range

and the next three lectures

of this course. I'll be going through

those measures of central tendency

and their associated measure of variability

in turn,

first the mode,

then the median,

then the me.