Measures of desperation.
Tell us about the spread of the data.
We'll be discussing three measures of discussion.
First is range, second is standard deviation and third is variance variance and standard deviation
are related by a simple formula that is variance is the squared of standard deviation.
Let's look at range first.
Range is simply the largest value, minus the smallest value.
So in that example, the largest value is 34 and the smallest value is seven.
So the range is 27.
But as we discussed, four main ranges influenced by outliers.
So if your data has outliers, range should be avoided, for example, in the state, only if you had
one value, which was exceptionally high, for example, its value was 150, then your range would be
150 minus seven, which will be 143.
But this range will not be a correct representative of the dispersion in this data, since only one
value is exceptionally high.
Other values are more or less confined to a small range, which is seven to 34.
To that way, if your data has outliers, try to remove the outliers before finding the range or else
don't use range as a measure of dispersion.
We will discuss this further when we are preparing our data for analysis.
So there will be a separate section on data prepossessing that will be discussing it in further detail.
Next, a standard deviation and variance variance is the average of square differences from the mean.
So explain this is the difference from the mean.
Where was the population mean?
As we defined earlier, X is the value of each observation.
When we do X minus MU, it is the difference of that particular observation from the mean we square
it all such differences and then we find the average of it.
When we do it for the population, we get a population standard deviation, for population standard
deviation, the formula is as per the definition only.
But if you are estimating standard deviation of population, this is a sample the formula has and minus
one below.
We will not discuss the proof of how this becomes a minus one.
But in short, this is because when we create all that possible sample, the standard deviation of all
these samples should come out to population standard deviation.
That will happen only when there is a minus one hit instead of in.
To just remember this, you could probably imagine that larger sigma value means data is more widely
distributed to.
Let's calculate the standard deviation for this data.
First, we have to calculate the mean mean for this data comes out to twenty four point eight and then
we find the variance which is defined as some of squared of distances from mean.
So what the first value, which is ten.
We find the difference from mean and we square it.
Then we take the second value, find the difference from mean, we square it and we add all these values
that we divided by the total number of observations, which is twenty four.
So we get sixteen twenty four point sixty five divided by twenty four, which comes out to sixty seven
point sixteen.
This is the variance.
We do a square root of this value to get standard deviation square root of sixty seven point sixteen.
Is it one, two, three.
So standard deviation for this data is eight point two three to the larger this value, the larger is
the dispersion from the center.
So if you get another set of twenty four observations which are similar mean but has lower value standard
deviation, that means that data has less dispersion in it and the values are closer to the mean.
And if you have a data which has just a division, the values are farther away from dimin to that's
all in this we do like to.