# What is Probability and Statistics in Mathematics?

In Maths, we have learned about various concepts. The fundamentals of Mathematics start with the number system and arithmetic operations. Apart from these, the other important branches are algebra, trigonometry, calculus, statistics, and probability. All these branches of mathematics are the core of mathematics. Each concept has its own importance in many fields.

Calculations and evaluation of mathematical problems using arithmetic operations are easy on a small scale but for larger data, we cannot use simple arithmetic. Hence, probability and statistics are the two important concepts that include real-time data and computations in big industries, like Business, Manufacturing, etc. Let us understand both the topics in this article here.

### What is Statistics?

The study of data analysis, data interpretation, data grouping, data collection, and organization is Statistics. Also, processing and presentation of data are defined under statistics. On large scale, industries where data is present in a huge amount, it is difficult to do the evaluation and making predictions. Therefore, stats are used to summarize the data by collecting them, so that they can be represented in a simpler manner.

The most important and common example of statistics is the population of the country. As we all know, any country’s economy, growth, and development are dependent on the population of the country. Therefore, statistics use the data and analyze it, to make the predictions of a better future for the country.

In Maths, we will come across, three major topics that are designated for statistical analysis. They are Mean, Median, and Mode. All together they are called a measure of central tendency.

• The mean is the average of the given data.
• Median is the middle value of the given set of data
• The mode is the value in a data-set, which is repeated the maximum number of times.

### What is probability?

Probability is the possibility of an event to occur. It represents the likelihood of the outcome of any random event. The extent to which an event is likely to occur is determined by probability.

A random event or random experiment is such an event whose outcome cannot be predicted.

Let us understand by example. Suppose if we flip a coin in the air, then what are the chances that a Head will appear? Here, either Head or Tail can appear as a possible outcome. Since there could be two results, hence the probability of getting a Head will be P(Head) = ½

Therefore, we can conclude that probability is equal to the ratio of the number of a favorable outcome and a total number of outcomes.

Probability is a vast topic, which covers various aspects. There are many theories and rules defined under this concept. One of the major aspects is probability density function, which defines the probability of a random variable. This random variable comes under a distinct range of values, from where we are objected to considering a single value. This function is used in large industries such as for modeling the diesel engine combustion.

Apart from these, there are various terminologies and concepts explained under statistics and probability, which are common to both the concepts random experiment, variance, mean, expected value, etc. Hence, both concepts are related to each other.