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Machine Learning - Data Description - Measures of Variation Variance and Standard Deviation
Oct 17, 2024
Machine Learning - Data Description - Measures of Variation Variance and Standard Deviation
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Measures of variation, variance and standard division
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So the variance is the average of the squares of the distance each value from its mean
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The symbol for the population variance is sigma square where sigma is the Greek letter and
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it is known as lower sigma and this is the lower case letter sigma
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And the formula for the population variance is x minus mu. whole square, sigma over it, and by capital n
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It will be denoted by sigma square. So this is known as population variance, where x is the individual value, mu is the population
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mean and capital n is denoting the population size. The standard division is the square root of the variance
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So the symbol for the population standard division is sigma. So the corresponding formula for the standard division will be
0:59
in case of population, that is sigma is equal to sigma squared spins, square root of that is
1:05
equal to this expression will remain the same, only the square root will be coming
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But in case of, in case of sample, if I want to calculate the respective variance here
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then in case of sample, it will be denoted by S square because S will be there for the sample
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S square, and here will be having small n minus 1, where small in is denoting the
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sample size. So, here that denominator will be having small n minus 1. So, similarly, the S
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square will be having the square root. So the standard division in case of population will
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be denoted by small s, and here it will be small n minus 1 in place of capital n
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So let us suppose if the X values are 35 45 30 35 and 40 25 So these are the values we are having So how many values we are having We are having these six values
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And then at first we are supposed to calculate the mean. So in that case, the mean has been calculated and it has been found as 35
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So now here we are calculating this x minus mu. So 35 minus 35, 45 minus 35
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In this way the values will get calculated. then you shall go for the square of that
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So, x minus mu whole square. So, here we are having the respective squares
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So now if you go on the addition, if you go on for the summation, we are getting 250 here
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So this is my variance. So in that case, 250 by 6, so 41.7, if I want to calculate the respective standard division
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so it will become 41.7 square root of that, it will become 6.5
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So, hence the standard division is 6.5 in this way we have calculated
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So now you can find that I'm just making one summary. In the previous video we found what is the range which is also the measures of variation
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So that is our range. So distance between the highest value and the lowest value and it can be represented by capital R
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And in case of variance, that is the average of the squares of the distances, that each value is
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from the mean. So, here in case of population, it will be expressed as sigma square in case of sample
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it will be s square. In case of standard division, there is a square root of the variance
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So in case of population, it will be sigma and in case of sample, it will be denoted by small s
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So, in this particular video, we have discussed how to calculate variance and the standard
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division and what are the different expressions of them in population and also in case if
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we apply them in case of sample. Thanks for watching this video
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