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In this video, we will discuss descriptive numerical measures which describe the center of the data.

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There are four values that they know decentered mean median Moore and mid-range.

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If you are aware about this, you can skip the lecture else, let us discuss them one by one.

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First is the also called average, it is obtained by adding all the values and then dividing by the

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number of values.

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The definition is pretty simple, but not these two delusions.

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One is population me and the other is Tamplin.

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If you want to find out the average height of, say, a hundred thousand people and you collect height

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of a hundred thousand people and find average, that is population mean.

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But if you think that this would be a difficult task and you collect it of only a hundred people assemble

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and find the average that averages sample mean.

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So population mean is denoted by Mbewe, the symbolism example, meaning is denoted by X Bar.

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Let's look at an example.

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Here are five students and their height.

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What is the meaning of their right to be at the height and divided by five?

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We get a twenty four divided by five, which comes out to one sixty four point eight.

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So if the glass contained only five students, this will be the population mean, but if the glass contained

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50 students and we were using the word of five students to calculate the mean, then this will be the

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sample mean because this is a sample of five students out of the 50 student, depending on what mean

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you are representing, you'll use the symbol here.

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If it is population mean, then you'll write music to 160 420.

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If it is sample when you write X bar is equal to one sixty four point eight.

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Next comes median.

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Median is the middle term when you order the data in increasing or decreasing order.

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So first step is to order the data and then we will find the middle.

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If the number of observations are ordered, then there will be a single random.

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And that would be odd million, but if the number of observations are even, then there will be two

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values in the middle.

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In that case, we will take average of the two middle values.

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Let's see an example again for the state of you'll find the median age.

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So first we order these in ascending order.

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And next, we find the middle value, which is the third value here, which comes out to 168.

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Suppose we have another student.

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Who has a height of 170 centimeters?

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That value will come a default position, in that case, there will be two values in the middle, 160

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and 170.

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There will have to average these two values to give the median, so the median in that case will be

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160 plus 170 by two, which will be 169 centimeters.

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Next is more.

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More value is the value which is occurring maximum number of times in the data.

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So if you consider probability, more value has the maximum probability of occurrence, not depending

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on the number of moles that the data has, it is given different names.

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If data has to modes, it is bimodal.

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If more than two modes, then it is multimodal or if no value is repeated and frequent is one for each

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value.

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Data has no more.

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Let's see an example.

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For this data, what is the mood hide?

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So since 168 comes to times and every other value is coming only once.

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168 is the here, if you go to the other data that we had when we calculated median, there is no repetition

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of any height.

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So this data has no more nexus, mid-range marriages.

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Very simple.

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You just find the average of largest and smallest values of your data to, for example, have the tallest

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one is 182 and shortages 155.

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Therefore, mid-range will be 155 plus 182 divided by two, which comes out to one sixty eight point

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five.

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So now we know the definitions of these measures of senator.

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Now, let us compare them, if you remember, we are using the image of a histogram and we have symmetric

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data like this, usually the mean median and mode will be identical.

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But if the data is skewed, like in the two images after this one, the three values will be different.

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Men will be highly influenced by the outliers here.

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Million will still be at the center.

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More will know the value with highest frequency.

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So which one stays relevant for us depends on the data in case we have outliers.

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We should either remove the outliers and then find something else, mediant would be our preferred measure

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of center over me.

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One advantage of Maude is that it can be concluded for qualitative, but also.

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So, for example, if we have categories like north, east, west, south, and we want to find out

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which category has the highest number of customers.

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We just find the mode categories, so we assign the number of customers to each category and then the

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more will be the category which has the maximum number of customers.

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This is a qualitative data that it has categories and numbers assigned to it.

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More can be found out for such data mean and median cannot be found out for such data, that is, you

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cannot have a mean of North-Western told.

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Also, if you are interested to know the probability of occurrence, Morde is still denoting the value

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which has the highest probability of occurrence.

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So these are the measures of center in the next video, we will discuss the measures of dispersion.