In cluster analysis, a ________ is a group of similar data points.

  • cluster
  • factor
  • matrix
  • model
In cluster analysis, a cluster is a group of similar data points. The goal of cluster analysis is to group, or cluster, observations that are similar to each other.

Bayesian inference is based on the principle of updating the ________ probability based on new data.

  • joint
  • marginal
  • posterior
  • prior
Bayesian inference works by updating the prior probability based on new data. This updated probability is known as the posterior probability.

What type of error can occur if the assumptions of the Kruskal-Wallis Test are not met?

  • Either Type I or Type II error
  • No error
  • Type I error
  • Type II error
Violation of the assumptions of the Kruskal-Wallis Test can lead to either Type I or Type II errors. This means you may incorrectly reject or fail to reject the null hypothesis.

What potential issues can arise from having outliers in a dataset?

  • Outliers can increase the value of the mean
  • Outliers can lead to incorrect assumptions about the data
  • Outliers can make data analysis easier
  • Outliers can make the data more diverse
Outliers, which are extreme values that deviate significantly from other observations in the data, can cause serious problems in statistical analyses. They can affect the mean value of the data and distort the overall distribution, leading to erroneous conclusions or predictions. In addition, they can affect the assumptions of the statistical methods and reduce the performance of statistical models. Hence, it's essential to handle outliers appropriately before data analysis.

What is the significance of descriptive statistics in data science?

  • To create databases
  • To describe, show, or summarize data in a meaningful way
  • To make inferences about data
  • To organize data in a logical way
Descriptive statistics play a significant role in data science as they allow us to summarize and understand data at a glance. They offer simple summaries about the data sample, such as central tendency (mean, median, mode), dispersion (range, variance, standard deviation), and distribution. They help in providing insights into the data, recognizing patterns and trends, and in making initial assumptions about the data. Graphical representation methods like histograms, box plots, bar charts, etc., associated with descriptive statistics, help in visualizing data effectively.

What are the potential issues with the K-means clustering method?

  • It cannot handle non-spherical clusters
  • It does not work well with non-numeric data
  • It is sensitive to outliers
  • All the options
The K-means clustering method can have several issues: it doesn't work well with non-numeric data, it's sensitive to outliers (since outliers can significantly move the cluster centroids), and it has difficulty handling clusters that are non-spherical or have varying sizes and densities.

In the context of a scatter plot, what does a positive slope indicate?

  • The correlation between the variables is weak
  • The variables are negatively correlated
  • The variables are positively correlated
  • The variables are unrelated
A positive slope in a scatter plot suggests that the two variables are positively correlated. This means as one variable increases, the other variable also tends to increase.

What is the impact of PCA on the interpretability of the original features?

  • It depends on the data
  • It doesn't affect interpretability
  • It enhances interpretability
  • It reduces interpretability
PCA typically reduces the interpretability of the original features. This is because each principal component is a linear combination of all the original features, making it difficult to understand how individual features affect the outcome.

What is the primary application of Bayes' Theorem in statistics?

  • To calculate the mean of a data set
  • To calculate the standard deviation
  • To determine if two events are independent
  • To update prior beliefs given new data
Bayes' Theorem is primarily used to update prior beliefs given new data. It's a way to go from a prior probability to a posterior probability, which is a more accurate estimate because it incorporates new evidence.

In hypothesis testing, a Type I error is committed when the null hypothesis is ______ but we ______ it.

  • False, fail to reject
  • False, reject
  • True, fail to reject
  • True, reject
A Type I error, also known as a false positive, occurs when we reject a true null hypothesis. This means we've found evidence of an effect or difference when there really isn't one.