## Statistics

Statistics is a living subject full of challenging problems and exciting developments. Through statistics, you would have the thrill of discovering, learning, and challenging your own assumptions. With statistics, new knowledge is created by pushing the frontier of what is known.

### The Power of Data

Data is all around us. The number of people in a country, sales figures of an organization, and the number of hits on a website are data that lets a business or a nation make informed decisions.

The field of statistics is all about learning from data. It is the process of converting raw data into a meaningful, organized, and informative form. Statistical knowledge is the base on which proper methods of collecting data, employing the right analysis, and effectively presenting the results are built. The discoveries in science and many predictions are all based on statistical methods. If you want to understand a subject deeply, you need to get into the statistics of it all.

If you are looking to learn and gather statistics notes, you must go through this article where you will learn the meaning and definition of statistics and the classification of statistics.

### Meaning and Definition of Statistics

Statistics means studying, collecting, analyzing, interpreting, and organizing data. Statistics is a science that helps to gather and analyze numerical data in huge quantities. With the help of statistics, you can measure, control, and communicate uncertainty. It allows you to infer proportions in a whole, derived from a representative sample. In other words, statistics could be described as the feature or characteristic of a sample and is generally used to estimate a population parameter's value.

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### The Need for Statistics

The early impetus for statistical data arose from the government’s needs for data like census and the need for information about various economic activities. In modern times, the necessity to turn large volumes of data available in many applied fields into meaningful and useful information has resulted in the evolution of both practical and theoretical statistics.

## Terms Used in Statistics

Statistics is applied in many real-life situations to make it easy to understand data when data is represented in a particular number (that represents all numbers). This number is termed as a measure of central tendency, and a few common central tendencies are:

### Mean

This is the average of given numbers and is measured by adding all the numbers and then dividing by the total count of numbers. So if a1, a2, a3, a4,...., an are n numbers then their mean \[\bar{a}\] = (a1 + a2 + a3 + …+ an)/n = \[\sum_{i=1}^{n}\] ai/n

### Median

If all the n numbers are arranged either in ascending or descending manner, then the middle number of that series denotes the median of the group. In the case of n being an odd number, the median is the observation at the ((n + 1)/2)th position. In the case of n being an even number, we get the median by taking the average of both the middle numbers i.e. the average of observations at (n/2)th and ((n + 1)/2)th observations.

### Mode

The mode of n numbers is the number that has the highest frequency in the given sample. In case there are no numbers that are repeated in the list, then that sample has no mode.

### Range

The range of observations is the difference between the highest and the lowest number in the list.

### Example Problem on Finding Mean, Median, Mode, and Range

From the list of values given below, let us find their mean, median, mode, and range.

12, 16, 13, 14, 13, 18, 14, 21, 13

Mean = 12 + 16 + 13 + 14 + 13 + 18 + 14 + 21 + 13/9 (since there are 9 numbers in the list) = 14.88

Median - To find median we will first write down the list in ascending order: 12, 13, 13, 13, 14, 14, 16, 18, 21

Here n = 9 so it is an odd number. So the median is the number at the position (9+1)/2 = 10/2 = 5. So, the median is 14.

Mode - Since the number 13 is repeated the maximum number of times (3 times) in the list, 13 is the mode of this sample.

Range - In the list the highest value is 21 and smallest value is 12 hence range = 21 - 12 = 9

## Classification of Statistics

Statistics has three broad categories as outlined below:

### Descriptive Statistics

This is the methodology where data is effectively collected, organized, and described.

### Inferential or Inductive Statistics

In this process, conclusions are drawn about unknown sample features taken from a population. This involves an interpretation of the descriptive stats.

### Predictive Statistics

This is the process where future values are predicted based on historical data.

## Application of Statistics

Statistics provides a clear picture of the work we do on a day-to-day basis, and it has wide applications in the following areas:

### Mathematics

We use statistical methods like probability and dispersion, to get more accurate information.

### Economic

Many economic parameters like the inflation of a country, employment status, exports and imports, etc. are all heavily dependent on statistical methods.

### Medical

Any drug is prescribed after it has been analyzed through statistics. Statistics measure the effectiveness of a drug.

### Psychology

Psychologists use statistics for figuring out things like peer pressure amongst youngsters.

### Education

In schools and colleges, lecturers use statistics to interpret which course their students are more interested in.

### Business

Business nowadays uses statistics to gauge customer preferences, product quality, target market, etc.

### Quality Testing

All the products a company produces goes through a quality check by employing statistical tools.

Banks decide to lend money to customers to increase the bank’s profits with a statistical approach to compare deposits and requests for loans.

### Astronomy

The size, distance, and other parameters of objects in the universe are measured using statistical methods.

### Weather Forecasting

To predict the upcoming weather, a statistical tool is used to compare previous and current weather.

Q1. What are the Different Types of Variables in Statistics?

Ans: There are two criteria on which statistical variables are classified:

**1. Nature of Variable**

Numerical - These are countable or measurable variables, for example, plant height, crop yield, etc.

Categorical - These variables cannot be measured, but they give qualitative data. For example the shape of leaves, the colour of flowers, etc.

**2. Source of Variable**

Primary data - The data that is found originally in the investigation process is called primary data. They are accurate and uniform data and need the supervision of an investigator. Collecting primary data is tedious, and many biological and experimental studies depend on primary data.

Secondary data - This is the data collected not by the investigator but some other person for their own use. They are usually data that is published by the primary investigator. Such data have vast use in agriculture, economics, public health, commerce, etc. A few examples are population census, budget records, annual rainfall, etc.

Q2. Who are Statisticians and What is their Role?

Ans: Specialists in the field of Statistics are called statisticians. They apply statistical methods and thinking to various endeavours that include business, social, scientific, marketing, education, genetics, etc. All the leaders of a country like military generals and lawmakers cannot make decisions or even get approval for their proposals unless they consult and take statisticians' help. For example, a pharmaceutical company will have to present loads of statistical data to a regulatory authority like FDA in the United States (EMA in the EU) to get their new drug approved.