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StarAgile

Published

Apr 10, 2023

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- What are Statistics?
- What are the sample and population in statistics?
- What is Descriptive Statistics?
- Example of descriptive statistics
- What is inferential statistics?
- How Do You Obtain A Random Sample?
- Example of Inferential Statistics
- Difference Between Descriptive and Inferential Statistics

Statistics are the backbone of any data analytics, so they are an important topic of study in data science training. Stats is a unit of mathematics that helps us identify patterns and trends in bulk numeric data. It can be categorised into two types, i.e., descriptive and inferential statistics. Here we will discuss the significant differences between descriptive and inferential statistics and their contribution to data analytics.

While statistics is a term almost everyone uses at some time or another in their daily life, it can be very easy to forget what it means and take it for granted. In simple words, statistics is an area of applied math that helps you collect, organise, interpret, analyse, and represent data. All of these steps are carried out in the process of data analytics. When statisticians use the term data analytics, they mean carrying out the statistical analysis of a single data set or data set.

Because of its importance in data analytics, statistics is subject in most Data Science Certification Courses and Data Science Training programs. Science or mathematics, psychology or marketing, medicine, statistics and its various techniques are needed in almost any field and industry, making data science training and other associate courses the most sought after. However, before heading into the dynamics of descriptive and inferential statistics, you may want to brush up on some of the terms you will frequently see in the rest of the post.

Sample and population are two basic concepts in statistics defined as follows.

The entire group that you want to draw information from and draw conclusions about is called a population. In daily life, the term population usually describes a group of people, for example, the population of a country or region. However, statistics refers to any group you are collecting information from. While it often refers to people, this term may also be used while studying objects, cities of the world, animals, colours, plants, etc. Exploring the entire population is not always possible, bringing us to the second term, “sample.”

A sample is a representative of a group of a larger population. Random sampling from various representative groups lets us draw broad conclusions about the overall population. This approach can also be called polling and is a popular way of collecting data. A pollster will ask a small group their views on a topic. This information can then be used to make an informed judgment about how the larger population thinks. This is an excellent way of collecting data as it saves time, hassle, and even the expense of extracting data from an entire population.

Descriptive statistics majorly defines the characteristics of a data set. It is a simple technique used to show, summarise, and describe data meaningfully. All you have to do is choose the group you are interested in, record data from this group, and use graphs and summary statistics to describe the group's properties. In this case, there is no uncertainty as you describe tangible items or people, and you can measure. The aim isn’t to infer properties about a more extensive data set.

Descriptive statistics may involve taking a sizable number of data points in the sample data and reducing them to various meaningful summary values and graphs. This process gives you insight and lets you visualise data instead of pouring through vast rough numbers. Descriptive statistics allow you to describe the entire population and individual samples. As this kind of statistic is explanatory, it is not heavily concerned with these two data types.

There are several parameters that description statistics look at. However, the following are the three important measures.

This measures the frequency of different outcomes in the sample or population. This can be represented as a table, numbered list, or graph. Visual representation of the information is more common as it can help you easily spot patterns or trends in a dataset.

This term measures the typical central values within the selected data set. Along with the central value, i.e., median, it also measures the average values of all the data points—mean and the value that appears the most in the dataset—mode.

Summarising these kinds of statistics is one of the first steps in determining other vital parameters of the dataset, like variability.

This is the third important measure in descriptive statistics; it can also be called the dispersion of a dataset. The variability of a dataset relies heavily on the central tendencies of the set. Variability is not just a single value as it is used to describe a range of measurements like;

**Standard Deviation:** it is the amount of variation or dispersion. Low standard deviation values indicate that most of the values in the set are close to the mean, and higher values indicate a broader range of values.

**Minimum and Maximum Values: **As the name suggests, these are the highest and lowest values in the dataset.

**Range: **This helps to measure the size of the distribution values. It is easy to determine simply by subtracting the smaller value from the larger one.

**Kurtosis: **This term is used to measure whether or not there are outliers or extreme values on the tails of the given distribution. If the tail does not contain an outlier, it is said to have low kurtosis, while those with many outliers are said to have high kurtosis.

**Skewness: **This is the term used to measure the symmetry of the given dataset. When you plot a bell curve, and the right-hand tail is longer and fatter, the data set is said to have positive skewness, and when the left-hand tail is longer and fatter, it is said to have negative skewness.

These values can help you gain surprising information about the given dataset when used together. Once you have a summary of the important statistics of a data set, it is easier to proceed to the next steps. This is the point at which inferential statistics comes into question.

If you want to describe the scores of around 30 students from a specific class, you would first record all the test scores before summarising the data and producing graphs to describe this data. Based on the scores achieved by the group, you can get collective information to get a good idea about the scores of the specific class.

Inferential statistics is where the focus is purely on making predictions about larger groups based on the representatives or samples of that population. As mentioned earlier, studying the entire population is not always feasible. In this case, a random sample is taken, and predictions about the population are made based on the information gathered from these samples.

This method allows you to study smaller groups instead of the entire population and make predictions rather than state facts. This is also why the results of inferential statistics are usually given in the form of probability.

But how accurate are these predictions? The accuracy of the prediction will depend on how accurate your samples are and how well they represent the entire population. This is why it is essential to take a random sample effectively. Any results based on non-random samples are usually useless and hence discarded. Random sampling is not a straightforward solution, but it is extremely important for anyone planning inferential techniques.

These are the fundamental principles of collecting a random sample.

Simply put, this s choosing the pool you want to draw your sample from.

Bigger sample sizes have more representatives of the overall population. However, a larger sample is difficult to work with as it is time-consuming and can even be expensive, and this was the reason behind choosing a sample in the first place.

Your sample size needs to be big enough that you are sure it represents the population. You will be confident in your results without being so small that it risks being unrepresentative and inaccurate.

After determining the ideal size for your sample, it is time to choose the actual sample by random selection. You can do this by using a random number generator, assigning every value a number and selecting these numbers randomly, or using similar algorithms and techniques.

Once the data sample is chosen, you can collect the data you need to infer information about the population. One point to remember is that a random sample only represents the population and is rarely 100% accurate.

While the list of inferential techniques you can use for analysing and gaining insight into the population is long, there are three main techniques that you should know.

This involves checking the samples multiple times to ensure you get the same results as your hypothesis. This is to ensure that your given results did not occur by chance.

These are used to estimate different parameters of measurement of the population based on your sample data. Instead of providing a single mean value, a confidence interval gives you a range of values given as percentages. Great examples of confidence intervals are scientific research papers that draw conclusions from a sample but always have a confidence interval along with the results. This kind of analysis is beneficial when measuring the degree of accuracy of a sampling method.

Both these techniques are used to observe how two or more variables correlate. It aims to determine whether a dependent variable gets impacted by one or more independent variables. It's used for predictive analytics and hypothesis testing.

Correlation analysis helps to measure the degree of association between two or more datasets. This does not give you a cause-and-effect result but is helpful in product sales predictions and other scenarios.

In the descriptive statistics example, we choose the score of a single class to study. If the same test has to be conducted using inferential statistics, we will study a larger population, such as 8th graders in a public school in your state. You would then devise a plan of getting random samples to ensure it properly represents all the students in that population. This process can be arduous as the students may sometimes be from different classes. Then, the analysis mentioned above can be carried out and inferences made.

While this entire post has been about descriptive and Inferential statistics, here is a quick recollection of the key differences between the two.

Descriptive Statistics | Inferential Statistics |

Accurately describes the features of the given population or sample | Uses samples to make generalisations about the larger population |

Organizes and presents in a purely factual manner | It can help you create estimates and predict any future outcomes |

Can present final results with the help of visual aids like tables, charts, or graphs | Can provide final results in the form of probability. |

Draws a conclusion based on the known data | Can conclude that the available data |

It uses different measures like distribution, variance, and central tendency. | It uses confidence intervals, hypothesis testing, and regression and correlation analysis techniques. |

Although both of these terms seem to be binary, they are usually used together. These powerful statistical techniques make up the backbone of data science and analytics fundamentals. If you find these topics exciting and want to make them part of your daily life, check out the Data Science certification course offered by Staragile. We are an Industry-Oriented company that provides a wide variety of professional and Data Science Training courses, including a Data Science Certification Course.

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