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### Introduction

Data science is a comprehensive blend of maths, business and technology. One has to go from data inference to algorithm development and then all the way to use available technology to draw the solutions for complex problems. At its heart, all we have is data. All our inferences can only be brought up once we start its mining. In the end, data science uses multiple mathematical techniques to generate business value present in the data for various enterprises

On a very broad level, data science comprises of 3 important components namely maths or statistics, computer science and information science. A very strong statistical background knowledge is necessary if one is to pursue a career in data science. Various organisations prefer data scientists with strong statistical knowledge as statistics is one important component providing insights to leading businesses worldwide

In this blog, we will understand 5 important statistical concepts for data scientists. Let us understand them one by one in the next section.

### Statistics and Data Science

Let us discuss the role of statistics in data science before beginning our journey into the math world!

In data science, you can always find statistics and computer science competing against each other for the ultimate supremacy. This happens, in particular, the areas concerning data acquisition and enrichment for predictive modelling

But somewhere, statistics have an upper hand as all the computer science applications in data science are more of it’s derivative

Statistics though is a key player in data science but not a solo player in any way. The real essence of data science can be obtained by combining statistics with the algorithms and mathematical modelling methods. Ultimately a balanced combination is required to generate a successful solution in data science

### Important Concepts in Data Science

#### 1. Probability Distributions

distribution of probabilities is characteristic that defines the likelihood that random variable can take feasible values. In other words, the variable values differ according to the fundamental spread of likelihoods.

Suppose you draw a random sample and are measuring the income of the individuals. You can start creating a distribution of income as you keep on collecting the data. Distributions are important in the scenarios where we need to find out outcomes with high likelihood and want to measure their predicted/potential values over a range

#### 2. Dimensionality Reduction

In machine learning classification problems, on the basis of which the final classification is done, there are often too many factors. These factors are essentially so-called characteristics variables. The greater the amount of characteristics, the more difficult it becomes to visualize and operate on the training set. Most of these characteristics are sometimes linked and therefore redundant. This is where algorithms for the decrease of dimensionality come into practice. Dimensionality reduction can be looked as a method or means of eliminating a large number of variables to reach a smaller subset or arriving at the variables which matter more than then others. It can be split into a choice of features and removal of features.

An easy email classification problem can be used to discuss an intuitive instance of dimensionality reduction, where we need to identify whether the email is spam or not. This can include a big amount of characteristics, such as whether or not the email has a specific name, the email content, whether or not the email utilizes a model, etc. Some of these characteristics, however, may overlap. In another situation, a classification problem based on both humidity and rainfall may collapse into just one fundamental function, as both of the above are highly linked. Therefore, in such problems, we can reduce the number of features.

#### 3. Over and Under-Sampling

In data sciences, we work with datasets representing some entities. It is required that all the entities have equal representation in the dataset which may not be the case every time. To cope with this, we have oversampling and undersampling as two measures in data science. These are data mining techniques and can modify unequal classes to create balanced sets. They are also known as resampling techniques

When one information category is the underrepresented minority group in the data sample, over-sampling methods can be used to replicate these outcomes for a more balanced quantity of beneficial teaching outcomes. Oversampling is used when there is inadequate information collection. SMOTE (Synthetic Minority Over-sampling Technique) is a common oversampling method that produces synthetic samples by randomly sampling the features of minority class events.

Also, If the information category is the over-represented majority class, undersampling can be used to mix this class with the minority class. Undersampling is used when there is an adequate quantity of information gathered. Common undersampling techniques include cluster centroids targeting prospective overlapping features within the gathered information sets to decrease the quantity of bulk information.

Simple duplication of information is seldom suggested in both oversampling and undersampling. Oversampling is generally preferable since undersampling can lead to the loss of significant information. Undersampling is suggested when the quantity of information gathered is greater than appropriate and can assist to keep information mining instruments within the boundaries of what they can process efficiently.

#### 4. Bayesian Statistics

Bayesian statistics is an alternative paradigm in statistics as compared to the frequentist paradigm. It works on the principle of updating a pre-existing belief about random events. The belief gets updated after new data or evidence about that data pops in

Bayesian inference revolves around interpreting probability as one measure to evaluate the confidence of the occurrence of a particular event.

We may have a previous faith about an event, but when the fresh proof is put to light, our beliefs are probable to alter. Bayesian statistics provide us with a strong mathematical means of integrating our previous views and proof to generate fresh subsequent beliefs.

Bayesian statistics have the capability of providing methods to update our beliefs pertaining to the occurrence of an event in the light of new data or evidence

This contrasts with another type of inferential statistics, recognized as classical or frequency statistics, which believes that probabilities are the frequency of specific random occurrences that occur in a lengthy sequence of repeated trials.

For example, when we toss a coin repeatedly, in case of tossing a coin, we can find that the probability of heads or tail will come up to value close to 0.5.

Frequentist and Bayesian statistics span over different ideologies. For frequentist statistics, outcomes are thought to be observed over a large number of repeated trials and then all the observations are made as compared to Bayesian where our belief updates with every new event

By offering predictions, frequentist statistics attempt to eliminate the uncertainty. Bayesian statistics attempt to maintain and refine uncertainty by adapting personal views with fresh proof

#### 5. Descriptive Statistics

This is the most prevalent of all types. It offers the analyst within the company with a perspective of important metrics and steps. Exploratory data analysis, unsupervised teaching, clustering and summaries of fundamental information are descriptive statistics. There are many uses of descriptive statistics, most particularly assisting us familiarize ourselves with an information collection. For any assessment, descriptive statistics are generally the starting point. Descriptive statistics often assist us to come up with hypotheses that will be checked subsequently with more official inference.

Descriptive statistics are very essential because it would be difficult to visualize what the information showed if we merely displayed our raw information, particularly if there were a bunch of them. Therefore, descriptive statistics enable us to show the information in a more significant manner, allowing the information to be interpreted more easily. For example, if we had the results of 1000 student marks for a specific student for the SAT exam, we might be interested in those students ‘ overall performance. We’d also be interested in spreading or distributing the marks. All the above-mentioned tasks and visualisations come under the idea of descriptive statistics

Let’s take an example here. Suppose you want to measure the demographics of the customers a retail giant is catering too. Now the retail giant is interested in understanding the variance present in the customer attributes and their shopping behaviours. For all these tasks, descriptive statistics is a bliss!

### Conclusion

In this blog, we had a look at 5 most important concepts in statistics which every data scientist should know about. Although, we discussed them in detail these are not the only techniques in statistics. There are a lot more of them and are good to know!

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