Business Analytics & Statistics

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Questions and Answers

Which type of analytics focuses on recommending actions to optimize business decisions?

  • Descriptive analytics
  • Diagnostic analytics
  • Predictive analytics
  • Prescriptive analytics (correct)

In statistical analysis, what does variance measure?

  • The number of data points in a dataset
  • The central tendency of a dataset
  • The square root of the mean
  • The dispersion of a dataset from the mean, measured in square units (correct)

According to the empirical rule, approximately what percentage of data falls within three standard deviations of the mean in a normal distribution?

  • 95%
  • 100%
  • 99.7% (correct)
  • 68%

According to the Chebyshev's formula, what is the minimum percentage of data that falls within 3 standard deviations from the mean?

<p>89% (C)</p> Signup and view all the answers

What does a coefficient of variation measure?

<p>A relative measure of dispersion relative to the mean (C)</p> Signup and view all the answers

What does covariance measure?

<p>The direction of the linear relationship between two variables (A)</p> Signup and view all the answers

In probability, what range of values is defined by Kolmogorov's axioms?

<p>0 to 1 (B)</p> Signup and view all the answers

What is the formula for conditional probability of event A given event B has occurred?

<p>$P(A \cap B) / P(B)$ (A)</p> Signup and view all the answers

Which of the following is an example of a discrete random variable?

<p>Number of hits on a website link today (C)</p> Signup and view all the answers

What type of variable can only be a whole number?

<p>Discrete variable (C)</p> Signup and view all the answers

Which distribution models the probability of the number of events occurring in a fixed interval of time or space?

<p>Poisson distribution (D)</p> Signup and view all the answers

In hypothesis testing, what does rejecting the null hypothesis indicate?

<p>There is sufficient evidence to conclude that the alternative hypothesis is correct (B)</p> Signup and view all the answers

What is a Type I error in hypothesis testing?

<p>Rejecting a true null hypothesis (A)</p> Signup and view all the answers

What is the level of significance?

<p>The probability of making a Type I error (D)</p> Signup and view all the answers

What statistical test is used primarily to determine if there is a significant difference between the means of two groups?

<p>t-test (D)</p> Signup and view all the answers

In regression analysis, what does $R^2$ represent?

<p>The coefficient of determination (D)</p> Signup and view all the answers

In the context of ANOVA, what is the null hypothesis?

<p>The means of all groups are equal (C)</p> Signup and view all the answers

What type of data is required for regression analysis?

<p>Numerical data (B)</p> Signup and view all the answers

What is data mining?

<p>The process of discovering patterns, trends, and useful insights from large datasets (B)</p> Signup and view all the answers

What is the goal of classification in data mining?

<p>To predict how to classify a new data element (C)</p> Signup and view all the answers

Flashcards

Descriptive Analysis

Looking at past performance and how it can be applied to business decisions.

Predictive Analysis

Using data to predict what will happen in the future.

Prescriptive Analysis

Recommends the best course of action based on data, using AI, machine learning, and algorithms to optimize decisions.

Discrete Metric

One that is derived from counting something.

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Continuous Metrics

Based on a continuous scale of measurement.

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Variance

Measures the dispersion of a dataset, calculated as the square deviation from the mean and measured in square units.

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Standard Deviation

The square root of the variance, measured in the units of the dataset; measures the spread of the dataset around the mean.

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Empirical Rule: 1 Standard Deviation

Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

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Empirical Rule: 2 Standard Deviations

Approximately 95% of the data falls within two standard deviations of the mean in a normal distribution.

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Empirical Rule: 3 Standard Deviations

Approximately 99.7% of the data falls within three standard deviations of the mean in a normal distribution.

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Chebyshev's Formula

A formula (1-1/k^2) determining the minimum proportion of data within k standard deviations of the mean.

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Coefficient of Variation

Provides a relative measure of dispersion relative to the mean; measured by standard deviation divided by the mean.

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Covariance

Measures the association between two variables by analyzing their linear associations.

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Correlation

Measures the strength and direction of the linear relationship between two variables; derived from covariance.

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Joint Probability

The likelihood of one or more events occurring simultaneously.

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Conditional Probability

The probability of one event occurring, given that another event has already occurred.

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Poisson Distribution

Models the probability of a given number of events occurring in a fixed interval of time or space.

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Type 1 Error

Rejecting the null hypothesis when it is actually true.

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Type 2 Error

Failing to reject the null hypothesis when it is actually false.

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Data Mining

Process of discovering patterns, trends, and useful insights from large datasets using statistical, machine learning, and database techniques to make data-driven decisions.

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