Now let us talk about descriptive statistics.
Descriptive Statistics is a summary statistic that quantitatively describes or summarizes the data.
So whenever we want to quantitatively summarize the data, we use the descriptive statistics.
We don't want to find out something out of the data.
We just want to summarize the data.
This is all descriptive statistics.
Now, while the scope of statistics is the process of using analyzing those statistics.
So the script, the statistics in the process of using and analyzing those statistics, we are just
trying to find out a summary of this in biostatistics, which we have, and we are trying to find those
and analyze these values.
We are not trying to do much out of it.
This is called descriptive statistics.
We just want to find out what type of data we have.
Measures of central tendency.
Mean is a calculated central value of a set of numbers to calculate a mean.
We add all the numbers and then divide it by the count of the numbers, which we have added.
The next measure of central tendency is the median.
Median is the middle number in a sorted in ascending or descending list of numbers.
The million is sometimes used as opposed to mean.
Then there are outliers in the sequence that might skew the average of the values.
Mode is a set of values in the values that appear the most often.
Let us see what these are in-depth.
So let us consider these odd values.
These are sorted and we have values as one, two, three, four, five, five, six, seven, eight,
nine and 12.
These are total order values.
The minimum value is one, while the maximum value is two.
In the range will be the maximum value minus the minimum value, which is 12 -111.
Now, let us go back to the definition of me.
Means that we add all the numbers and divide the sum by the count of the number added.
So we add all of these values.
So we add one plus two plus three, four plus five plus five plus six plus seven plus eight plus nine
plus two it.
And then divide the sum by the total number of values which represent.
So we have one, two, three, four, five, six, seven, eight, nine, ten, 11 values in total.
So we divide the sum by 11.
So here the mean is 5.60.
Now let us find out the media as we have discussed.
Median is the median most value.
So that might be the most valuable.
We.
293847565
is the middle most value.
So out of 11 values.
The six value comes out to be the middle most value, which is the median.
The next value is more.
Mode, as the definition says, is the value, which appears most often.
So he is out of all of these values.
Five appears twice, which is most often.
So mode is five.
Now please note that when we are calculating median for the old values, the median is the middle most
value.
I mean, is all a sum of all the values divided by the thought of the values.
Right now.
Let us come to the end of the day.
Now, here we have all the violence which will present in these old values.
And additionally, we have an outlier value hundred.
This outlier value means that this value is something very different from the original sequence, which
we have.
So for these values, the minimum number is one.
The maximum number is 100.
The range will be 100 minus one, which is 99.
Mode still remains five because five is the maximum opening value.
Now median is the by the mean of the middle two values.
So the sum of the middle most values, which is five and six.
Because these are even number of values.
So there will be two values in the middle.
So five and six.
So we add five and six and divide it by two to find out the average of these two values, which is the
median of the even values.
So one thing which we find out is that median of even values is some of the median values divided by
two.
By median of the old values is the middle most number.
Now, in case of finding out the mean, we saw that when we have these 11 values out of these 11 values,
when we found out the mean, it came out to be 5163, because these values are near to each other.
Now, just by the presence of one outlier, the mean value has changed a lot.
I've added all these values.
One divided by 12.
To find out the meaning of these even values.
So this comes out to be 13.5.
Line here, the mean was 5.63.
This means that presence of even one outlier causes a very huge change in the value of meme.
So we cannot really explain the sequence using the meme because when I see the meme of these values
is 13.5.
I am kind of seeing that the median value is hit between 12 and 100 but is not correct because the majority
of the values which are lying from values with.
Should have been around 5.60.
So which is the reason why we cannot really use these measures of central tendency to explain much?
So when the value such as the mean is calculated in presence of an outlier, it cannot really depict
the measure of central tendency more so in this particular situation.
We will try to explain the sequence or explain the data using median value.
Because the median value will not be impacted by the outlier much.
So here when an outlier was added, still the median did not change much.
It is still 5.5.
I'm here.
The median was five.
So by adding one outlier, still the median remains almost the same and did not change as much.
The mean that.
Now which value to use when.
So mean is highly impacted by outliers.
Just what we saw here.
I'm median is robust against outliers, which is the reason why we when we have outliers present, then
instead of using me, we can better in the data using median.
And what is the value that is most likely to be some?
So when we are taking a sample of a population, then the value of the mode will be something which
will be something the most number of times.