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#### Define Statistical Analysis: Formulas Of Different Methods One Can Use For Performing It

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### Statistical analysis.

In the context of the business intelligence, statistical analysis is the process of collecting and analysing the every data sample in a set of the items from which samples can be drawn. Here, the sample shows the representative selection drawn from a total population.

In other words, the statistical analysis is the science of collecting, exploring and representing large amounts of data to discover underlying patterns and trends. The other definition of the statistical analysis is “Statistical analysis is the process of generating statistics from stored data and analysing the results to deduce or infer meaning about the underlying dataset or the reality that it attempts to describe.” While, the statistics is defined as the “the study of the collection, analysis, interpretation, presentation, and organization of data.” That’s basically the same as the definition of data science, and in fact the term data science was initially coined in 2001 by Purdue statistician William S. Cleveland in the title to his paper “Data Science: An Action Plan for Expanding the Technical Areas of the Field of Statistics.”

The statistical analysis can be done by performing the further mentioned five steps. The first one is to describe the nature of the data to be analysed. Secondly, by exploring the relation of the data to the underlying population. Third one is the creating a model to summarize understanding of how the data relates to the underlying population. Fourth step is to prove the validity of the model and the last step includes the employment of the predictive analytics to run scenarios that will help to guide the future actions.

While, the goal of the statistical analysis is to identify trends. For example, a normal small retail shop can use the statistical analysis to find the trend of the unstructured or semi – structured customer data that can help the firm to understand the pattern of their customer and to increase the positive customer experience as well as helps to increase the sale of the firm.

State and describe the definition and formulas of different methods one can use for performing it.

Staring from the probability and statistical distribution, through basic concepts of statistical inferences, to a collection of the methods of useful for the scientific research. It contents the high number of the diagrams, table and examples along with the theoretical justification of the methods of an analysis introduced. The followings are the most commonly used method of performing the statistical analysis: -

1. Descriptive Statistics

The descriptive measures are those which indicates where the centre or the most typical value of the valuable lies in collected set of the measurements are called measures of the centre. This measures of centre are often referred to as averages. There mainly consist with the three methods those are mean, median and mode. The median and mode can only apply to the quantitative data while the mode can be used with the quantitative and qualitative data.

• Mode: - The sample mode of the qualitative or a discrete quantitative variable is that value of the variable which occurs with the greatest frequency in a data set. The more appropriate definition of the mode can be define as the “Obtain the frequency of each observed value of the variable in a data and note the greatest frequency. 1. If the greatest frequency is 1, then the variable has no mode. 2. If the greatest frequency is 2 or greater, then any value that occurs with that greatest frequency is called a sample mode of the variable.”

To calculate the mode of the variables, the first step is to construct the frequency distribution for the data using classes based on the single value. After that the mode can be easily determined by the frequency distribution.

The following is the formula of the mode: - Where,

l = Lower Boundary of modal class

h = size of the model class

fm = Frequency corresponding to modal class

f1 = Frequency preceding to modal class

f2 = Frequency proceeding to modal class

• Median: - The sample median of a quantitative variable is that value of the variable in a data set that divides the set of observed values in half, so that the observed value in one half are less than or equal to the median value and the observed value in one half are less than or equal to the median value and the observed values in the other half are greater or the equal to the median value and the observed value in the other half are greater or equal to the median value. The proper definition of the median is “Arrange the observed values of variable in a data in increasing order. If the number of observation is odd, then the sample median is the observed value exactly in the middle of the ordered list. If the number of observation is even, then the sample median is the number halfway between the two middle observed values in the ordered list.”

The formula for median is the follows: - Where,

N = Number of terms.

• Mean: - This is the most commonly used measures of the centre for the quantitative variable. The definition of mean is “The sample mean of the variable is the sum of observed values in a data divided by the number of observations.”

The formula of the mean is as follows: - Where,

∑ xi = the sum of all numbers

n = the number of numbers

xi = numbers.

There are various other methods of the statistics analysis those are Probability, Statistical Inference, Hypothesis Testing, Linear Regression, Correlation, One – Way Analysis of Variance, Two Way Analysis of the Variance, Analysis of Covariance and Non Parametric Statistics. Apart from the above methods there are various other methods are also present to perform the statistics analysis of the observations.

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