
Explore probability through the classical approach, defining p as favorable outcomes over total outcomes using coins, dice, and cards, and link this method to binomial, Poisson, and normal distributions.
Explore the basics of probability, defining an event and calculating its likelihood as favorable outcomes over total cases, with deck-of-cards examples and replacement versus without replacement scenarios.
Explore probability concepts using the binomial distribution to compute 'at least k' successes, update prior to posterior probabilities, and apply to manufacturing quality and risk scenarios.
Explore the Poisson distribution and its use in calculating event probabilities, compare it with the binomial distribution, and apply these concepts to real-world data analytics scenarios.
Explore distributions, compare normal and Poisson models, and assess reliability using standard deviation to estimate probabilities of program completion times.
Explore how correlation measures the degree of relationship between variables, including positive, negative, perfect, and spearman's rank correlations, and learn regression for forecasting with independent and dependent variables.
Explore how to determine the degree of relationship between variables using direct correlation methods. Identify and interpret positive and negative correlations across observations.
Explore correlation using the assumed mean method to estimate relationships in data analytics, addressing biases and interpreting observations with mean-based calculations.
Develop the product-moment approach to measuring correlation, deriving the X squared and XY terms, and applying the formula to assess relationships in data analytics.
examine correlation in grouped series by analyzing frequency across cities and square-mile values, revealing positive and negative patterns in desegregation observations.
Apply rank correlation to analyze differences across six schools and cities using a formula and a small set of observations.
Explore rank correlation and Spearman's methods in the same ranks case for data analytics. The lecture emphasizes computing and interpreting rank-based measures for data relationships.
Investigate correlation of concurrent deviations by analyzing positive and negative signs across data series, deconstructing columns, and applying a step-by-step comparison framework.
This lecture introduces regression as a forecasting tool in data analytics, building least-squares regression equations that relate independent and dependent variables, and interpreting regression and correlation coefficients.
Explore regression analysis using the method of least squares to estimate relationships between variables, build a regression line, and forecast values from observed data.
Derive the regression equation and regression coefficients from data, using x values, deviations, and sums of squares to compute the slope and forecast outcomes.
Explore regression analysis using regression equations to solve systems of equations, interpret x and y variables, and apply standardized procedures in data analytics.
Explore measures of central tendency, including mean, median, and mode, and dispersion such as range and standard deviation, with practical frequency calculations.
Analyze measures of central tendency by exploring means, frequency concepts, and their formulas, including cumulative frequency, to understand how data center around the average.
Analyze quartile deviation alongside foundational dispersion measures such as range and frequency, including cumulated frequency, to interpret data distribution.
Explore mean deviation in data analytics by calculating deviations using numeric examples and basic arithmetic operations.
Examine the standard deviation, its formula, and how it relates to variance and data spread. Discuss frequencies, evolution of standard deviation, and five times standard deviation guideline.
Explore index numbers as tools to measure changes in price, quantity, and value, including fixed-base and chain-based methods, inflation and deflation, and practical calculation basics.
Learn how index numbers measure economic activity and price changes, including inflation, rising prices, and shifts in exports and imports.
Explore how index numbers measure price changes over time and analyze how price movements relate to aggregate demand, using past-year data.
Explore index numbers and their price relationships through the core formula, examining spot price movements and time-based price comparisons in data analytics.
Statistics is the specific branch of science from where the Data Analysts bring distinct conclusion/interference under the same data. Moving discussion a step further, we shall discuss Important Statistical Techniques like:
Probability
Probability Distributions-Binomial, Poisson & Normal Distribution
Regression Analysis
Correlation Analysis
Index Numbers
Measures of Central Tendency & Dispersion
Statistical Data Analysis
Being a branch of science, Statistics incorporates data acquisition, data interpretation, and data validation, and statistical data analysis is the approach of conducting various statistical operations, i.e. thorough quantitative research that attempts to quantify data and employs some sorts of statistical analysis. Here, quantitative data typically includes descriptive data like survey data and observational data. In the context of business applications, it is a very crucial technique for business intelligence organizations that need to operate with large data volumes. The basic goal of statistical data analysis is to identify trends, for example, in the retailing business, this method can be approached to uncover patterns in unstructured and semi-structured consumer data that can be used for making more powerful decisions for enhancing customer experience and progressing sales. Apart from that, statistical data analysis has various applications in the field of statistical analysis of market research, business intelligence(BI), data analytics in big data, machine learning and deep learning, and financial and economical analysis.
Basics Steps for Statistical Data Analysis:In order to analyze any problem with the use of statistical data analysis comprises four basic steps:
1. Defining the problem
The precise and actuarial definition of the problem is imperative for achieving accurate data concerning it. It becomes extremely difficult to collect data without knowing the exact definition/address of the problem.
2. Accumulating the data
After addressing the specific problem, designing multiple ways in order to accumulate data is an important task under statistical data analysis. Data can be collected from the actual sources or can be obtained by observation and experimental research studies, conducted to get new data.
In an experimental study, the important variable is identified according to the defined problem, then one or more elements in the study are controlled for getting data regarding how these elements affect other variables.
In an observational study, no trial is executed for controlling or impacting the important variable. For example, a conducted surrey is the examples or a common type of observational study.
3. Analyzing the data:Under statistical data analysis, the analyzing methods are divided into two categories;
Exploratory methods, this method is deployed for determining what the data is revealing by using simple arithmetic and easy-drawing graphs/description in order to summarize data.
Confirmatory methods, this method adopts concept and ideas from probability theory for trying to answer particular problems.
Probability is extremely imperative in decision-making as it gives a procedure for estimating, representing, and explaining the possibilities associated with forthcoming events.
4. Reporting the outcomes:By inferences, an estimate or test that claims to be the characteristics of a population can be derived from a sample, these results could be reported in the form of a table, a graph or a set of percentages. Since only a small portion of data has been investigated, therefore the reported result can depict some uncertainties by implementing probability statements and intervals of values. With the help of statistical data analysis, experts could forecast and anticipate future aspects from data. By understanding the information available and utilizing it effectively may lead to adequate decision-making. (Source)
The statistical data analysis furnishes sense to the meaningless numbers and thereby giving life to lifeless data. Therefore, it is imperative for a researcher to have adequate knowledge about statistics and statistical methods to perform any research study. This will assist in conducting an appropriate and well-designed study preeminently to accurate and reliable results. Also, results and inferences are explicit only and only if proper statistical tests are practised.