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Master the Law of Total Probability: Key Concepts Explained

College Statistics: Master Data Analysis & Probability

Basic Concepts

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Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Census and bias

Census and Bias

Classifying Bias

Data Representation

Frequency distribution and histograms

Frequency polygons

Shapes of distributions

Data Interpretation

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Bivariate, scatter plots and correlation 

Regression analysis

Equation of the best fit line

Probability

Addition rule for "OR"

Addition Rule for "OR"

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability with permutations and combinations

Probability involving permutations and combinations

Law of total probability

Law of Total Probability

Probability of a randomly selected employee meeting a sales target

Probability of a randomly selected driver being involved in an accident

Probability of a randomly selected customer making a purchase

Probability of a randomly selected person being overweight

Bayes' rule

Bayes" Rule

Bayes rule

Bayes" rule

Bayes' Rule

Discrete Probabilities

Probability distribution - histogram, mean, variance & standard deviation

Binomial distribution

Binomial Distribution

Mean and standard deviation of binomial distribution

Interpreting Mean and Standard Deviation of Binomial

Poisson distribution

Poisson Distribution

Geometric distribution

Negative binomial distribution

Negative Binomial Distribution

Determining the Negative Binomial Distribution

Determining the Cumulative Negative Binomial Distribution

Hypergeometric distribution

Determining the Cumulative Hypergeometric Distribution

Hypergeometric Distribution

Properties of expectation

Properties of Expectation and Variance

Properties of Expectation

Normal Distribution and Z-Scores

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

Sampling distributions

Understanding Proportions and Sample Size

Central limit theorem

Central Limit Theorem

Applying the Central Limit Theorem

Rare event rule

The Rare Event Rule for the Central Limit Theorem

Confidence Intervals

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Chi-Squared confidence intervals

Chi-Squared Confidence Intervals

Confidence intervals to estimate population mean

Student's t-distribution

Student"s t-distribution

Determining a Confidence Interval for a Population Mean using t-distributions

Hypothesis Testing

Null hypothesis and alternative hypothesis

Proving claims

Confidence levels, significance levels and critical values

Test statistics

Traditional hypothesis testing

Traditional Mean Hypothesis Testing

P-value hypothesis testing

Proportion Hypothesis Testing

Chi-Squared hypothesis testing

Variance Hypothesis Testing

Chi-Squared Hypothesis Testing

Mean hypothesis testing with t-distribution

Hypothesis Testing Mean Claims without Knowing <katex> \sigma </katex>

Analysis of variance (ANOVA)

Chi-square goodness of fit test

Type 1 and type 2 errors

Type 1 and Type 2 Errors

Set Theory

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

<p>Get better math marks with our complete Statistics help &ndash; be it Introduction to Statistics, Probability and Statistics, Elementary Statistics, or Business Statistics. We&apos;ve got you all covered!</p>

<p>Just like your class or textbook, our comprehensive help includes topics such as Descriptive statistics, Inferential statistics, Hypothesis testing, Probability, Regression, T test, Standard deviation, and more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest statistics problems. Then, strengthen your understanding with tons of statistics practice.</p>

<p>All our lessons are taught by experienced Statistics teachers. Let&apos;s finish your homework in no time, and ACE that final.</p>


College Statistics

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math

<h2>What is Statistics?</h2>
<p>Statistics &ndash; a word you are probably familiar with and less fearful of than "linear algebra" or "calculus". Broadly and colloquially speaking, statistics is often used to describe a synthesized, mathematical, summary of a topic. So for example, one might ask Google what are the summary statistics of the age groups in the USA that suffer from mental illness. More specifically, statistics is a special branch of mathematics that involves the study of datasets. Statistics can be classified into two major groups: descriptive statistics and inferential statistics. Descriptive statistics is the arm of statistics that analyses datasets largely by providing quantitative summaries and big-picture visualizations. Inferential Statistics on the other hand involves analysing only a random sample of data from a larger dataset. Conclusions are then drawn from the larger dataset based on what/how the random sample dataset informs.</p>
<p>Put together, these two divisions of statistics undergo the following general process: data is collected, analysed, interpreted, and illustrated. The goal of data analysis is usually rooted in hypothesis testing. To truly test hypotheses, a series of statistical tests are ensued (e.g. T-test, Chi-square Test) so that we can assess a number of elements about the data such as confidence intervals, probabilities, probability distributions, and so forth. Once we have results, we interpret our findings and assess the implications - <a href="https://www.studypug.com/blog/hunger-games-the-pursuit-of-gamification-in-math-education/">how can we use the data to make improvements, adjustments and advancements?</a> These results tend to be more easily digestible through visual aids (e.g. Frequency Histograms)</p>
<p>While under the umbrella of mathematics, statistics is actually found in multiple disciplines and a mandatory requirement for multiple degrees. Here at StudyPug we are here to help with all kinds of university statistics under the sun! With 1000&apos;s of lessons and 24/7 help you can count on us! So whether you are beginning introduction to statistics, or need help with probability and statistics for engineering and sciences, or feel stuck with business statistics problems, we want to let you know you have come to the right place!</p>

<h2>Is University Statistics hard?</h2>
<p>At StudyPug we understand that aside from learning how to adult, juggling several responsibilities, and constantly running out of time and resources, university life in general feels incredibly hard. University statistics, however, does not have to an additional burden of difficulty. Like many other challenges you will face in your post-secondary academic journey, university statistics will be trying, but not overbearing. At StudyPug we offer Statistics help for all kinds of University statistics online 24/7. Our lessons are carefully catered for all levels starting from University Statistics for dummies up to complex applications of statistics in university statistics courses like business stats, engineering or sciences stats. Our highly experienced and knowledgeable stats tutor will guide you through all the statistics review you will require to boost your aptitude and confidence in being able to solve increasingly complex questions. So whether you are struggling with basic concepts in permutations and combinations, or can not figure out when to use an ANOVA in lieu of linear regression to analyse a dataset, we are well prepared to help you overcome these challenges at your own pace and in your own time! With our resources close at hand, you&apos;ll soon discover in no time how effortless it is to crack the tough topics and resolve the difficult questions.</p>

<h2>How do I use StudyPug to learn University Statistics?</h2>
<p>A great question &ndash; there is a lot of content that we cover so where do you begin? So far so good, you have made it this far by visiting us here at <a href='[[region_textbook.html|{"textbook_key":"university-statistics"}]]'>https://www.studypug.com/university-statistics</a> and dropping down to the course index here we will be able to set your bearings straight. If you are looking for an online statistics course to guide and compliment your learning for university statistics classes, or perhaps you are someone who is hoping to get ahead of the game and ensure that you are well prepared for university statistics, our lessons are for you.</p>
<p>Begin by browsing through the topics you passed on your way down here to the course index. While every topic is available to you right away, you can take comfort in the fact that we have organized it in succession, building on the most fundamental concepts (recommend for experts and Stats for dummies alike) you will require to progress through the advanced topics.</p>
<p>Once you have honed in on a topic, begin watching the lesson that addresses your burning questions &ndash; be it from stats homework or a concept you covered in a previous lecture. We will take you through step-by-step examples to ensure you understand how the concepts actually plays out in different problems and to teach you how to apply your knowledge as well as timesaving hints and tips. Again, keep in mind that you might need to backtrack to an earlier lesson or topic to fully master the content you are trying to understand. Still feel like you need to dig deeper? We cover some core concepts in our other <a href='[[region_textbook.html|{"textbook_key":"statistics"}]]'>statistics course</a> that will supplement your learning of the bare necessities required to excel in university statistics. This course is available to you for no additional expense so take advantage of our truly one of a kind, comprehensive, online, stats study guide!</p>
<p>Last but foremost, we encourage you to practice. Each lesson is immediately followed by a series of practice questions we have designed for you. Practice is so important because it confirms your understanding of the lesson through active learning, exposes you to a wide variety of questions, and gives you confidence to move forward to the next lesson. Practice questions are always available to you so dive right into our repository of practice questions if you are simply looking to gain more practice with a type of question, or concept you already have a strong understanding of.</p>

<h2>How to pass University Statistics?</h2>
<p>Finals creeping up on you? Feeling unprepared for that mid-term exam or stats test? Perhaps you have given up all hope of passing and have settled on a z-score. Fear not, at StudyPug, we strive to make learning stats online stress-free, straightforward and simple.</p> 
<p>StudyPug offers the best university statistics help out there hands down! Get a grip of those nerves, take a deep breath, and jump straight in and learn statistics online with the best statistics tutor on the Internet! We are available to you 24/7 so whether you are caught up cramming all night or feel like you need to catch up over spring break, our goal is to assist you in passing your university statistic course!</p>
<p>Let us start by advising you to delve into one of our many statistics tutorials that will cover all the pertinent topics, walk you through statistic examples, and several types of questions you will likely encounter throughout your university statistic course. We will make sure your revision is thoroughly complete; so that you will be getting all the university statistics help you need here at StudyPug. No need to look elsewhere for help with statistics online! But do not stop there &ndash; exercise your learning through application. We have over 150 unique practice questions for you to discover, offering you easy practice for your statistics exam prep. Complete as many, if not all the questions that we have prepared for you! This is the key to strengthening your knowledge and skills to gain the assurance that you are well prepared to pass your university statistic course. Feeling stuck? Simply slip back into one of our lessons and quickly refresh your memory on how to tackle similar kinds of questions. Then take another shot at our practice questions again and don&apos;t give up!</p>
<p>Now repeat this process over and over again - begin with a topic you are really struggling with as you will know that it may take longer to revise. Alternatively, begin with simpler concepts and use this to motivate you as you progress through these more quickly. We will have you geared up to pass that final, mid-term, test, or exam in no time!</p>

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