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## Statistical Application of R & Python: Know Skewness & Kurtosis and Calculate it Effortlessly

This is a blog which shall widen your approach on the Statistical Application using R & Python. You perhaps already have been calculating Geometric Mean using R & Python and are already aware of the Application of Harmonic Mean using R & Python. However, if you are eager to further your knowledge about Skewness & Kurtosis and interested to know of their application using R and Python, then this is the right place.

#### Skewness:

Skewness is a metric which tells us about the location of my dataset. That is, if you want to know where most of the values are concentrated on an ascending scale.

Skewness is of two kinds: Positive skew and Negative skew. A positively skewed dataset will have most of the values concentrated at the beginning of the scale. Eg: If a woman is asked to rate 100 tinder profiles based on the looks on a scale of 1 – 10, 1 being the ugliest and 10 being the most handsome. Then the resulting ratings will be positively skewed. This is to say that women are harsh critiques of looks.

Now, consider another example: Say if the wealth of the 1% richest people were to be plotted on a scale of say \$0 – \$200 billion. Then, most of the values will be concentrated at the end of the scale. This will be an example of a negatively skewed dataset.

In essence, skewness is the third central moment about mean and gives us a feel for the location of the data set values. It is recommended to go through STATISTICAL APPLICATION IN R & PYTHON: CHAPTER 1 – MEASURE OF CENTRAL TENDENCY to have an understanding of the Central Tendency and its measures. Having no skewness will mean the data set is fairly symmetrical and has a bell shaped curve.

Where n is the sample size, Xi is the ith X value, X is the average and S is the sample standard deviation.  Note the exponent in the summation.  It is “3”.

#### Kurtosis:

Kurtosis is a statistical measure that’s used to describe, or Skewness, of observed data around the mean, sometimes referred to as the volatility to volatility. Kurtosis is used generally in the statistical field to describe trends in charts. Kurtosis can be present in a chart with fat tails and a low, even distribution, as well as be present in a chart with skinny tails and a distribution concentrated toward the mean.

Kurtosis for a normal distribution is 3.  Most software packages use the formula:

The types of kurtosis are:-

#### Application:

A person tries to analyze last 12months interest rate of the investment firm to understand the risk factor for the future investment.

The interest rates are:

12.05%, 13%, 11%, 18%, 10%, 11.5%, 15.08%, 21%, 6%, 8%, 13.2%, 7.5%.

Here is the table:

 Months(One Year) InterestRate (%) April 12.05 May 13 June 11 July 18 August 10 September 11.5 October 15.08 November 21 December 6 January 8 February 13.2 March 7.5

#### Calculate skewness & Kurtosis in R:

Calculating the Skewness & Kurtosis of interest rate in R, we get the positive skewed value, which is near to 0. The skewness of the interest rate is 0.5585253.

The kurtosis of the interest rate is 2.690519

Kurtosis is less than 3, so this is Platykurtic distribution.

#### Calculate Skewness & Kurtosis in Python:

Calculating the Skewness & Kurtosis of interest rate in Python, we get the positive skewed value and near from 0. The skewness of the interest rate is 0.641697.

The kurtosis of the interest rate is 0.241602.

Kurtosis is less than 3, so this is Platykurtic distribution.

#### Conclusion:

Firstly, according to the output of the data the value is positively skewed(R & Python), positive skewness indicates a distribution with an asymmetric tail extending toward more positive values.

And the kurtosis is less than 3 (R & Python), it is a platykurtic distribution. Positive kurtosis indicates a relatively peaked distribution. And the distribution is light tails.

Secondly, the value of the skewness and kurtosis are different in R and Python, but the actual effects are more or less the same. The results are different because skewness and kurtosis are calculated with different formulae or method for the measurement like Bowley’s measure, Pearson’s(First, Second) measures, Fisher’s measure & Moment’s measure. And different software (ex. R, Python, SAS, Excel etc) using different processes to calculate skewness & kurtosis brings the same ultimate result. The numerical values change only when the numbers are also changed. So, we sometimes get different results.

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## Hacking is Wide and Dangerous in India, CBI Reports

The recent conference organized by the Central Bureau of Investigation on Cyber forensic notes that over 22,000 websites were hacked in India between April 2017 – Jan 2018. Not the best of the news for the nation which is largely counting on their citizens to be tech-savvy.

In the conference, CBI disclosed of its plans to build a cutting edge Centralised Technology Vertical (CTV) to fight crimes, voiced by Minister of State for Personnel, Jitendra Singh. The CTV is a huge project involving around Rs 99 crore, which will not only share the real-time information about the cyber attacks but also of the perpetrators.

From young superintendents of police to top brass of security agencies, police forces, law enforcement officers and the Intelligence attended this conference and discussed about the alarming rise of cybercrimes throughout the country.

#### The Major Issue

Jurisdictional issues were a main problem and hit greatly on the investigation in these cases because most of the incidents of cybercrimes are triggered from foreign lands. Though the total loss of money from the recent cybercrimes weren’t disclosed, some debilitating cases in cybercrimes were dicussed once again, which included the loss of USD 171 million from union Bank of India’s Swift.

#### To End it

To lessen the magnitude of the cybercrimes, the CBI is on their way towards reinforcing them with the state of the art technology. Besides, you can also take up courses in PHP, HTML, Python Certification Training in Delhi, to be informed of the trending languages and be future proof.

## Application of Mode using R and Python

Mode, for a given set of observations, is that value of the variable, where the variable occurs with the maximum or the highest frequency.

This blog is in continuation with STATISTICAL APPLICATION IN R & PYTHON: CHAPTER 1 – MEASURE OF CENTRAL TENDENCY. However, here we will elucidate the Mode and its application using Python and R.

Mode is the most typical or prevalent value, and at times, represents the true characteristics of the distribution as a measure of central tendency.

#### Application:

##### 245

[Note: Here we assume total=245 when we calculate Mean from the same data]

#### Calculate Mode in R:

Calculate mode in R from the data, i.e. the most frequent number in the data is 51.

The number 51 repeats itself in 5, 7 and 8 phone calls respectively.

#### Calculate Median in Python:

First, make a data frame for the data.

Now, calculate the mode from the data frame.

Calculate mode in Python from the data, i.e. the most frequent number in the data is 51.

The number 51 repeats itself in 5, 7 and 8 phone calls respectively.

Mode is used in business, because it is most likely to occur. Meteorological forecasts are, in fact, based on mode calculations.

The modal wage of a group of the workers is the wages which the largest numbers of workers receive, and as such, this wage may be considered as the representative wage of the group.

In this particular data set we use the mode function to know the occurrence of the highest number of phone calls.

It will thus, help the Telephone Exchange to analyze their data flawlessly.

Note – As you have already gone through this post, now, if you are interested to know about the Harmonic Mean, you can check our post on the

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## Calculating Geometric Mean Using R and Python

In this blog, we are going to discuss the Geometric Mean and its application using Python and R.

Geometric Mean of group of ‘n’ observations is the nth root of their product. It is defined only when all observations have the same sign and none of them is zero.

#### Calculate the Geometric Mean of the salary increment of 12 employees. From the following table, calculate the average salary increment of the year (2019-2020):-

 Name Salary Increment inPercentage (%) Ritesh 10.09% Heena 15.45% Kritika 9% Anuradha 13.06% Gaurav 20% Prakash 14% Aarti 16% Meena 6.25% Utkarsh 12.85% Chirag 10% Neha 18% Smrita 21.36%

#### Calculate the Geometric Mean in R:

So, from the data of the employee’s in R we calculate the G.M. and get that the average salary increment in the year (2019-2020) = 13.17618 or 13.18% (approx).

#### Calculate the Geometric Mean in Python:

First, make a data frame in Python from the following table.

Now, calculate the Geometric Mean from the data-frame.

So, from the data of the employee’s in Python we calculate the G.M. and get that the average salary increment in the year (2019-2020) = 13.176183416401196 or 13.18% (approx).

We use Geometric Mean for calculating ratios, rates and percentages. And it is not affected by the extreme value or outlier. In this particular problem, we use Geometric Mean because an average of the salary increment of the employee’s not affected by the extreme highest or extreme lowest value, that’s why the salary increment rates of Meena and Smrita do not have any effect on the total average rate.

Geometric Mean gives small value than Arithmetic Mean.

Note: This is a continuation of the blog: Statistical Application in R & Python: Chapter 1 – Measure of Central Tendency. It would be better to go through the first installment and then read this one. More blogs are to be followed, so stay tuned.

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