Statistics Learning Centre presents:
Understanding summary statistics.
Hi, I'm Dr Nic, and in this video, I'm going to tell you about,
"Summary statistics."
There are many videos and resources that explain
how to calculate summary statistics.
But this video won't do that.
This video is about what summary statistics
A data set is made up of variables and observations.
We may want to summarise the distribution of values for each of the variables.
Often, we wish to compare two groups within a set of data.
We should always use graphs to explore and analyse the data.
You can see how to do this in our video, analysing and commenting
on graphical output, using "OSEM."
When we explore data, we are interested in:
Position, spread, shape, and special.
In this video, we will mainly talk about position.
To summarize the position or location of the data,
we use the mode, median, or mean.
We will illustrate this with an example.
Here is a dotplot of the number of pairs of shoes 161 students said that they owned.
Each dot corresponds to one person and indicates
how many pairs of shoes that person said they owned.
When we summarize, we look at the overall distribution and ask,
"What would be a typical number?"
If someone asked you, how many pairs of shoes do these students own,
there are several possible answers.
For now, we're only going to allow a one number answer.
A single indication of position or location.
10 is one possible answer.
25 people said that they own 10 pairs of shoes.
More people said they had 10 pairs of shoes than any other number.
This is called the mode.
Another possible answer is 7. It is the number in the middle
of the distribution. It is called the median.
There are 161 students represented in our data set,
so halfway is student number 81.
There are 80 students above and 80 below.
That student in 81st place said he or she had 7 pairs of shoes,
so the median is 7.
The other summary value is often called the average,
though the more technical term is the mean.
Sometimes, average refers to the median so it is safer to use the term, mean.
If we piled all the pairs of shoes together,
and distributed them evenly over the 161 students,
they would end up with 10.07 pairs each.
The mean number of pairs of shoes per student is 10.07.
In this case, the mean is close to the mode.
But this is only sometimes true.
For this set of data, the mean is quite a lot higher than the median.
That is because there are a few people who own a whole lot of shoes.
When their shoes are spread around, they cause the mean number of shoes
per person to go up. We will talk more about this later.
When we report statistics, we need to decide which summary values
are most indicative of the distribution of the data.
To illustrate this, let's have a look at what happens
when we separate out the students into female and male.
You can see that the two distributions look quite different from each other.
For the female students, the mode is 10, the median is 12, and the mean is 15.73.
For the male students, there are two popular values, 4 and 6,
there is no mode.
The median is 5, and the mean is 6.43.
In both cases, there are just a few people
who have a whole lot more shoes than the others.
If those extreme values weren't there, the means would drop to 12.86 and 5.8,
which are closer to the medians.
In both cases, when we remove the extreme values,
the median does not change.
In these examples, the median gives a better indication
of the position or location of the distribution.
Whenever you summarize the location or position of the data,
you will need to decide which is the most appropriate statistic.
You need to look at a graph of the data,
and think about the context, in order to make this decision.
This video is brought to you by Statistics Learning Centre.
Visit our website for more resources to help you learn.