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As data becomes increasingly essential to business decision-making, data scientists and analysts need to understand the fundamentals of statistics to make sense of data and extract valuable insights. This article will provide an introduction to the fundamentals of statistics for data analytics and data scientists.
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In data analytics, statistics is used to derive insights and knowledge from data to inform business decisions. Understanding the fundamentals of statistics is essential for data scientists and analysts because it helps them to identify patterns, trends, and relationships in data.
There are two types of statistics: descriptive statistics and inferential statistics.
Descriptive statistics is used to summarize and describe a dataset. It provides information on the distribution, central tendency, and variability of the data. The most commonly used measures of descriptive statistics include the mean, median, mode, range, variance, and standard deviation.
Inferential statistics is used to make predictions or draw conclusions about a population based on a sample of data. It involves estimating parameters, testing hypotheses, and determining the statistical significance of relationships between variables.
Statistics is essential for data analytics because it enables data scientists and analysts to:
To understand statistics for data analytics, it is important to be familiar with some fundamental terms used in statistics:
Probability is the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.
Population and Sample
A population is the entire group of individuals or objects a researcher is interested in studying. A sample is a subset of the population that is used to make inferences about the entire population.
Distribution of Data
The distribution of data refers to how the data is spread out or clustered. The most common distributions are normal, uniform, and skewed.
The Measure of Central Tendency
The measure of central tendency is used to describe the central or typical value of a dataset. The most commonly used measures of central tendency are the mean, median, and mode.
Variability refers to how spread out the data is. The most commonly used measures of variability are the range, variance, and standard deviation.
Central Limit Theorem
The central limit theorem states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal if the sample size is large enough.
Conditional Probability and P-Value
Conditional probability is the probability of an event occurring given that another event has already occurred. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true.
Significance of Hypothesis Testing
Hypothesis testing is used to determine whether a difference between two groups or variables is statistically significant or due to chance.
A random variable is a variable whose value is subject to chance or randomness. It can be discrete or continuous.
Probability distribution functions (PDFs)
A probability distribution function is a function that describes the probability of occurrence of each value of a random variable. It can be discrete or continuous.
Mean, Variance, Standard Deviation
The mean is the average value of a set of data. The variance is the average of the squared differences from the mean, and the standard deviation is the square root of the variance.
Covariance and Correlation
Covariance measures how two variables change together. Correlation measures the strength of the linear relationship between two variables.
Bayes theorem is a mathematical formula that calculates the probability of an event occurring based on prior knowledge or information.
Linear Regression and Ordinary Least Squares (OLS)
Linear regression is a statistical method that analyzes the relationship between two variables by fitting a linear equation to the observed data. OLS is a method of estimating the parameters of the linear regression model.
The Gauss-Markov theorem states that under certain conditions, the ordinary least squares (OLS) estimator is the best linear unbiased estimator (BLUE).
Parameter properties (Bias, Consistency, Efficiency)
Bias refers to the difference between the expected value of the estimator and the true value of the parameter. Consistency refers to the property that the estimator approaches the true value as the sample size increases. Efficiency refers to the property that the estimator has the smallest variance among all unbiased estimators.
A confidence interval is a range of values that is likely to contain the true value of a parameter with a specified level of confidence.
Hypothesis testing is a statistical method used to determine whether a hypothesis about a population parameter is supported by the sample data.
Statistical significance refers to the likelihood that a result or relationship observed in the data is not due to chance.
Type I & Type II Errors
A Type I error occurs when the null hypothesis is rejected when it is true. A Type II error occurs when the null hypothesis is not rejected when it is false.
Statistical tests (Student’s t-test, F-test)
The Student’s t-test is a statistical test used to determine if the means of two groups are significantly different. The F-test is a statistical test used to determine if the variances of two groups are significantly different.
p-value and its limitations
The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result if the null hypothesis is true. It has limitations and should be interpreted in conjunction with other measures of statistical significance.
Statistics is an essential tool for data analysts and scientists to make informed decisions based on data. Here are some of the applications of statistics in data analytics and data science:
In conclusion, statistics is an essential tool for data analysts and data scientists, and it plays a crucial role in various aspects of data analytics and data science. Using statistical methods, data analysts and data scientists can gain insights into large datasets, make informed decisions, and predict future trends. Therefore, it is essential for data analysts and data scientists to have a fundamental understanding of statistics to succeed in their careers.
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