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Statistics and Probability is the branch of Mathematics which deals the predictions, decide among two options, creating hypothesis. Now a day’s statistics has become one of the important in data science. Due to high demand in data science, combined training as been provide to students. Statistics and Probability are building blocks of many new technologies in recent world. It has been used in Artificial Intelligence and Machine Learning to make foundation to all such technologies.

Definition of Statistics:- It is the branch of Mathematics which deals with the gathering, interpretation, analysis and presentation of masses of numerical data.
Statistics is the collection of Quantitative data.

Types of Variables

There are mainly two types of variables

  1. Categorical/li>
  2. Numerical

These two main variables again divided into two types

  1. Categorical:- Categorical data comes under Qualitative data. The data combined into categories by their properties is called as categorical data.
    1. Nominal:- This Categorical variable has two or more categories with any formal ordering. This is also called as unordering list.
    2. Ordinal:- It is defined as the variables that has two or more categories with clear order is known as Ordinal variables.
  2. Numerical
    1. Interval: :-Numerical Variables has order with equal interval. It is same as Ordinal variables.
    2. Ratio:- It is the interval data with zero point. Example of ratio Variables are Height, Weight, temp in Kelvin.

Normal Distribution

It is one of the important of all the probability distributions. It has directly applied to various real problems and many useful distributions are depends upon it.
Normal Distribution is the probability methods that tells how the values of the variables are distributed. Example of Normal distribution data is Height.

Parameter of Normal Distribution

  1. Mean: - It defines the peak value of the normal distribution. It is the central tendency of distribution.
  2. Standard Deviation: It defined the width of the normal distribution. SD is the Measure of variability.
Characteristics of Normal Distribution
  1. The main characteristics of Normal distribution is Mean, Mode, Median are close to each other..
  2. Mode is near to the center of distribution and almost symmetrical.
  3. The shape of normal distribution is approximately flat on top, decrease quickly then decrease more toward the tails of the distribution.
  4. Sampling and Combination of Variables

    Sampling: - It is the process of taking sample from population for measurement or counting. The sample will be random. The samples of all the same size having same probabilities has been selected from population.
    Variance is always positive quantity. So, any variance value multiplied by the square of constant must have positive.

    Central Limit Theorem: - In the probability, Central limit tells that distribution of sample means approximates a normal distribution. In the statistics, Central Limit Theorem states that provided a proper large sample size from population with fixed level of variance.
    According to CLT, the mean of the sample of data is nearer to mean of the overall population in question. Central Limit theorem show phenomenon with average of standard deviation and sample mean equal to population mean and deviation.

    Conditions for Central Limit Theorem

    Before applying Central Limit Theorem, there are some conditions which require to fulfill.

    1. Randomness: - Independent sample must be taken. It should show a random sample from the population or at least follow population distribution.
    2. Large Sample Size: - Must be large sample size n so that the np >= 10 and nq>=1.
    3. 10% Rule: - Entire population must be in range of 10% of the sample size.
    What is Quantitative Analysis?

    It is the process of gathering and examine measurable and verifiable data such as market share, wages and revenues in order to know the performance and behaviour of business.

    Quantitative Analysis Techniques
    1. Regression Analysis: - It is the general technique which has been used by economist and statisticians other than business owner. Regression Analysis take the statistical equations to predict the impact of one variable over another variable. It is sued to calculate the interest rates affected consumer’s behavior in respect of assets investment.
    2. Linear Programming:- It is the process of taking several linear inequalities belongs to some conditions and finding the best value comes under those conditions. The common purpose of solving the Linear Programming is to graph inequalities to form a walled-off area on x-y plane.
    Design of Experiments (DOEs)

    It is the well structured and planned process which has used to calculate the relationship between various factors that affects a project and several outcomes of project. The Design of Experiments was stated by Sir Ronald A. Fisher. The Design of Experiments generally used for research and development purpose to optimize the issue occurred in resources.

    Experimental Design: - The main aim of the Experimental Design is to take proper quantitative details about the impact of several treatments and their common interactions. The principles of Experimental design are randomizations, replication, covariance analysis and use of factorial designs. The statistical methods of analysis and design of experiments are generally model dependent.

    Sampling Theory: - The main objective of sample surveys is to collect the details about particular fixed population by predicting finite population parameters like fractions, means and totals. The observation comes from sampling units are considered as fixed in the sampling theory. Statistical methods from sampling theory can be count as distribution free.

    Sample Distribution

    A sample distribution is the graph of statistics of sample data. In the sampledistribution some common terms come like Mean, Range, Standard Deviation, Unbiased prediction of variance, variance of sample and Mean absolute value of the deviation.

    Standard deviation of sample distribution of Proportion

    The standard deviation of sampling distribution of proportion (P) is nearly combinedto the binomial distribution. It is one of the special cases of sample distribution.

    Sample Proportion

    Sample Proportion is the random sample of object n taken from the sample of population P. If we consider x objects has particular properties then sample proportion p is the p =x/n.

    Descriptive Statistics

    It is the summary descriptive coefficients that brief a provide data set which will be shown the full or sample of certain population. The Descriptive Statistics are divided into measures of central tendency and measures of spread. In the central tendency like mean, mode, median and standard deviation comes.

    Measures of Descriptive Statistics

    It is seen that all the descriptive Statistics measures the central tendency or variability measures which is called as dispersion. Measurement of variability gives the spread-out distribution for set of data. Where as central tendency measurement explained the center position of distribution for particular set of data.

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