Machine Learning - Data Description - Measures of Central Tendency: Mean, Median and Mode

Now, we shall discuss measure of central tendency mean median mode

So, a statistic is a characteristic or measure obtained by using data values from a sample

So, always remember, statistic will be a characteristic or measure for a sample

And a parameter is a characteristic or measure obtained by using all the data values from

a specific population. So, statistic will be related with the sample and parameter will be related with the population

At first we are going to discuss mean. So the mean is the sum of values divided by the total number of values and the symbol

will be represented as this. So whenever we are trying to calculate the mean, so the symbol represents the sample

mean is this one. So that is x bar is equal to x1 plus x2 up to x n, then by n, and then by n, and the symbol

and that can be also written as sigma x by n, where n represents the total number of values in the sample

So always remember whenever we are trying to calculate the mean for a sample, it will be expressed in the form of x bar

So now in case of population, the mean will be calculated, and in that case, it will be expressed in the form of mu

So here we are having this x1 plus x2 up to xN, the addition will be done by capital n, here it was small n

where small n was the size of the sample and here it is capital n so that is sigma x by

capital n for a population the greek letter mu is used for the mean where capital n represents

the total number of values in the population so now let us suppose the procedure for finding

the mean for group data is given below so here we are having the respective classes so these are the lower class boundary this is the upper class boundary so these are the lower class boundaries and these are the upper class boundaries And that is the respective frequency

here we are having. So now what you shall do, we shall calculate the midpoint. So how do

to calculate the midpoint? That is a lower class boundary plus upper class boundary whole by two

So here you have calculated the midpoint and this is the respective frequency. So B and

the columns are to be multiplied to get the column D that is f into xM so in this way

you are getting the sum of that that is 490 and then 490 by the sum of the

frequencies so here the sum of the frequency is 20 and there is 24.5 miles will

be the respective mean for this given data so whenever we are having our data in

the form of divided or in case of classified in multiple different classes

then how to calculate the mean we have shown that one. Next one we are going to discuss the weighted mean

So find the weightage mean for weighted mean for a variable capital X by multiplying each

value of its corresponding weight and dividing the sum of the products by the sum of the weights

So here you can find that here we are having multiple values x1, x2 dot a dot x n and the respective

weight values are w1, w2, dot, dot, up, and the respective weight values are w1, w2, dot, up, and the respective weight values to w n. So here we shall go for the sum of the product terms. So w1 x1 plus w2 x2 plus dot-da-dot

In this way we'll be continuing up to w n x n and the full summation, the full total

will be replaced or will be divided by this sum of the all weight edges. So in this way the

expression will be sigma w xx by sigma w So where w2 dot dot up to w n are the weights and x1 x2 dot dot x n are the respective values Now let us go for one example here So English composition 1 introduction to psychology biology biology 1 and physical education

So here we are having four different courses and the respective credits and the weightage values

are given here. And here we are having the respective grades, that means the A, C, B and D

So, we have written the respective points for which this grade has been obtained by a student

So in that case, if you want to calculate the respective weighted mean, then it will be calculated

using that formula. So whatever you have derived. So that is a 3 into 4 plus 3 into 2 in this way and this is the sum of the weightages

and we are getting the average as 2.7. So the grade point average is 2.7

Now we are going for the median calculation. The median is the midpoint of the data array

The symbol for the median is capital M, capital D, MD. So let us go for one example

The number of cloudy days for top 10 cloudiest cities is shown below

So find out the median one. So median is the midpoint of the data array

There is a symbol for the median will be MD. So we have discussed that one

So what will happen here we are having the set of say 10 such values we are having

first we can arrange those values we can arrange those values and in that case as we are having

10 number of data and 10 is the even number so i cannot get the middle most one but let us suppose

the last value is missing and we are having nine data here then obviously the fifth value

after arranging them in the shorted form in the ascending order and in that case we are having

the fifth value will be the median in that case so if this 240 is not present if we're having 9

values here then 1 2 3 4 5 so the 5th data will be the median but here the case is not like that here we having 10 such data so obviously for 10 data as 10 is even I

not going to find out the middle most value in that case I shall consider these two

values and then I shall calculate the median considering their average so median

that is MD will be equal to 213 plus 2 223 hold by 2 that is 218 hence the median is

is two and eight days. Now here we are going to calculate the mode. The value that occurs

most often in a data set is called the mode. So, let us go for one example. Find the

mode of the signing bonuses of 8 nFL. So players for a specific year. So the bonuses in

millions of dollars are given here. So if you judge this particular value, you might be

getting the value 10 which is having the frequency highest that is 10 has occurred for�

so solution it is helpful to arrange the data in the order although it is not necessary in

case of mode calculation so now what will happen if we go on ordering this data you can find

that the same data will be coming adjacently so here you can find that 10 million occurred

three times a frequency larger than any other number so the mode is dollar 10

millions in this particular case. So, sometimes it may happen that all the data are having

the occurrence one only. In that case, I can say there is no mode available in that data set

Sometimes it may happen that two data are having the same highest frequencies. In that case

we can call that this particular data set is bimodal. So, in our video, we have discussed

how to calculate the mean for sample and population, mode, and also the median

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