Statistics is a mathematical branch of mathematics which deals with the collection, analysis, interpretation or explanation, and presentation of data. Statistics is sometimes considered a separate mathematical science instead of a branch of mathematics. Whereas data is used in many scientific investigations, statistics is associated with using data in the context of uncertainty and making decisions in the face of uncertainty.

### Statistics

Statistics is a branch of mathematics that studies the collection, analysis, interpretation, presentation, and organisation of data. Statistics is primarily used to improve data understanding and focus on specific applications. The process of gathering, analysing, and summarising data mathematically is recognised as statistics. Statistics were first associated with state science, in which they were used to collect and analyse information about a country’s economy, population, and other factors. In mathematical statistics, linear algebra, differential equations, mathematical analysis, and probability theories are all used.

### Descriptive Statistics

Using measures of central tendency and measures of dispersion, the descriptive statistics technique is used to represent the data collected and summarise the data and its attributes.

### Inferential Statistics

To gather conclusions from data, the above statistical strategy is employed. To make inferences, inferential statistics uses statistical tests on samples, and it does so by identifying differences between two groups.

### Measures of Central Tendency in Statistics

The foundations of descriptive statistics are the assessment of central tendency and the assessment of dispersion. The representative value for the given data is a measure of central tendency which tells us how data points are centred. It is done in order to see how the data is distributed around the centred metric. The mean, median, and mode are used to find the central measures of tendency. In our daily lives, we see average student height, average wealth, average exam results, and average player height.

### Mean, Median and Mode in Statistics

The arithmetic average of a data set is calculated by multiplying all of the numbers in the set by the number of observations. Regardless of whether the data is presented in ascending or descending order, the median is the middle number in the set. Eventually, the median is the number which appears the most in a data set and is in the middle of the range.

### Statistic topics for CAT

The mathematical statistics prerequisite should cover the following topics:

- Basic set theory notation and combinatorics
- Definitions and properties of probability
- Discrete and continuous distributions are both common.
- Bivariate probability distributions
- Probability with conditions
- Variance, expectation, and random variables
- Transformations, both univariate and bivariate
- Random variable convergence: in probability, in distribution, almost certain
- Laws of Large Numbers, Central Limit Theorem
- Bias, MSE, consistency, sufficiency, maximum likelihood, method of moments, and other estimation terms Fisher Information, UMVUE, Rao-Blackwell Theorem
- Hypothesis testing: power and significance level Likelihood ratio tests, Neyman-Pearson lemma
- Confidence interval definitions and duality with hypothesis tests

### List of CAT sections with the most weightage

The relative importance of different Quant topics shifts over time. Previously, the “number system” was a very important topic, but now Arithmetic has taken the place and is more important than any other subject. As a consequence, generalising this response is extremely difficult. The test pattern from the previous three to four years remains unchanged.

- Numbers (Factors, LCM/HCF, Remainder, Unit Digit, etc.)

2.Arithmetic

Proportion & Ratio

Profit & Loss & Percentage

Alignment, Average

Solution & Mixture

Time, Distance, and Speed

Work and time.

- Geometry and Mensuration (Triangles, Circles, Quadrilaterals)

Algebra Coordinate Geometry Trigonometry .

4.Linear Equation

Inequalities in Quadratic Equations

Sequence and Series of Modulus (AP/GP/HP)

- Permutation & Combination Function & Graph Logarithm

Set theory and probabilities.

### How To Prepare For Statistics related topics For CAT exam

Read each problem carefully.

Every word and symbol matters in a statistics problem, so there could be a lot of statistical facts to consider. To get all of the information you need, read the problem slowly and several times. Mark the problem if required. Make a note about what each part of the equation represents and what you are attempting to solve for.

### While studying, use a pencil and paper.

Even if the book gives you the answer, if you get to parts of the text which describe a concept or formula, work them out yourself alongside the book. Working through the problems as you study can help you really build the concepts you’re learning before you move on to solving problems on your own.

### Solve more problems

For each statistical concept you learned that week, your instructor will most likely assign homework with a few problems. If you find one concept extremely hard, solve 2 or 3 additional problems based on that concept. Becoming good at statistics necessitates actually solving problems, so more practice is always beneficial.

### Conclusion

The science of data collection and organisation is recognised as statistics. The results are interpreted using an analysis that includes measures of central tendencies and measures of dispersion. The frequency distribution of data is represented using bar graphs, histograms, pie charts, stem and leaf plots, line graphs, and ogives. It is possible to collect quantitative (numerical: discrete and continuous) or qualitative data (categorical). Probability and statistics assist students in gaining access to their analytical and mathematical abilities. It is an important portion of the CAT curriculum.