Image:Statistics in machine learning
Image:Statistics in machine learning

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Standard and Variance Deviation

In this post, we’ll examine the measurement of data variability in more detail. You’ll master the fundamentals of standard deviation and variance in the classes that follow. This piece follows the last post in the series, where we learned how to quantify and depict data distribution.

Variance in Machine Learning

Variance is defined as the average of the squared deviations from the mean.

Let’s first look at some data set, where we have a list of 12 incomes, to better grasp what it represents.

There is an extreme value (an outlier) of 100,000 that raises the mean to 40,200 and widens the range to 175,000, however, the majority of the values are concentrated between 15,000 and 35,000.

Now, referring to the preceding concept, let’s compute the variance. The square of each point’s deviation from the mean will be added, multiplied by the number of values in the collection, and then divided. 

Commonly, the variance is denoted by the Greek letter Sigma squared (2). The following equation can be used to determine the variance.

Where n is the total number of terms in the set, is the mean, and x stands for each term in the set. You will learn more about this in the Bootcamp coding courses at Edureify.

Variance Example:- 

Variance is another number that expresses how to extend (arrange) out the values 

For example, if you take the square root of the variance, you get the standard variation!

The other way is, if you multiply the standard deviation by itself, you get the variance!

Find the mean:

(90+98+100+89+86+95+97) / 7 =     93.57

Find the difference from the mean for each value:

90 – 93.57 = -3.57

98 – 93.57 =  4.43

100 – 93.57 =  6.43

 89 – 93.57 = -4.57

 86 – 93.57 = -7.57

 95 – 93.57 = 1.43

 97 – 93.57 =  3.43

Find the square value:

(-3.57)2 = 12.7449

 (4.43)2 = 19.62

 (6.43)2 = 41.344

(-4.57)2 = 20.884

(-7.57)2 = 57.3049

(1.43)2 =   2.044

 (3.43)2 =  11.7649

Find the variance of the average number of these squared differences:

(12.7449+19.62+41.344+20.884+57.3049+2.044+11.7649) / 7 = 23.672.

Standard Deviation in Machine Learning

Finding the standard deviation is rather simple after determining the variance. It is the variance’s square root. Recall that the variance is represented by the number 2? The symbol for the standard deviation is denoted by π.

There is a faster approach to discovering the variance as well. Please verify the following equation.

Obs: You’ll see that I set the argument to zero and that I used it. Avoid the trouble. Delta Degrees of Freedom, or ddof, is what Python Pandas gives us the variance normalized by n — ddof, and ddof is defined as 1 by default. If you had set ddof to zero, then the standard variation will be equal to zero 

The definition of standard deviation-The standard deviation is a measure of how the values are distributed.

A low standard deviation indicates that the majority of the data are within a small range of the mean value or average value.

A high standard deviation indicates that the data fall within a wide range.

Example: This time, we recorded the ages of older individuals, but we only counted seven of them.

age = [86,87,88,86,87,85,86]

0.9 is the standard deviation.

The standard deviation and variance form a great part of the online coding courses at Edureify. You can enroll and know more about it through Edureify, the best AI learning app. The various machine learning principles including Azure learning, Machine learning algorithms, No Code Learning, and A- Z statistics of machine learning have already been discussed by Eduriefy in earlier articles. You can refer to all of them for overall knowledge. 

Some Frequently Asked Questions

Q:- What are standard deviation and variance in machine learning?

Ans:- Variance. Variance is another number that indicates how spread out the values are. If you take the square root of the variance, you get the standard deviation! Or the other way around, if you multiply the standard deviation by itself, you get the variance!

Q:- What is the difference between variation and standard deviation?

Ans:- Variance is the average squared deviations from the mean, while standard deviation is the square root of this number. Both measures reflect variability in distribution, but their units differ: Standard deviation is expressed in the same units as the original values (e.g., minutes or meters).

Q:- Does standard deviation mean more variation?

A:- Standard deviation is the square root of the variance. The variance helps determine the data’s spread size when compared to the mean value. As the variance gets bigger, more variation in data values occurs, and there may be a larger gap between one data value and another.

Q:- Why do we need a variance and standard deviation?

A:- Variance helps to find the distribution of data in a population from a mean, and standard deviation also helps to know the distribution of data in a population, but standard deviation gives more clarity about the deviation of data from a mean.

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