Statistics Quiz: Measures of Central Tendency and Variability

Descriptive Statistics

• Measures of Central Tendency:
  • Mean: average value of a dataset
  • Median: middle value of a dataset when arranged in order
  • Mode: most frequently occurring value in a dataset
• Measures of Variability:
  • Range: difference between the largest and smallest values
  • Variance: average of the squared differences from the mean
  • Standard Deviation: square root of the variance

Inferential Statistics

• Hypothesis Testing:
  • Null Hypothesis (H0): a statement of no difference or effect
  • Alternative Hypothesis (H1): a statement of difference or effect
  • Test Statistic: a numerical value used to determine the significance of the results
  • P-Value: the probability of observing the test statistic assuming the null hypothesis is true
• Confidence Intervals:
  • A range of values within which a population parameter is likely to lie
  • Margin of Error: the maximum amount by which the sample statistic may differ from the population parameter

Probability

• Basic Concepts:
  • Experiment: an action or situation that can produce a set of outcomes
  • Sample Space: the set of all possible outcomes of an experiment
  • Event: a set of one or more outcomes of an experiment
• Rules of Probability:
  • The probability of an event is a number between 0 and 1
  • The probability of the sample space is 1
  • The probability of the empty set is 0
  • The probability of the union of mutually exclusive events is the sum of their individual probabilities

Data Visualization

• Types of Plots:
  • Histogram: a graphical representation of a frequency distribution
  • Box Plot: a graphical representation of the distribution of a dataset
  • Scatter Plot: a graphical representation of the relationship between two variables
• Data Visualization Best Practices:
  • Clearly label axes and titles
  • Use color effectively to convey information
  • Avoid 3D plots and unnecessary embellishments

Descriptive Statistics

• Measures of Central Tendency: values that describe the middle of a dataset
  • Mean is sensitive to outliers, and is affected by extreme values
  • Median is the middle value when data is arranged in order, and is resistant to outliers
  • Mode is the most frequently occurring value in a dataset, and a dataset can have multiple modes
• Measures of Variability: values that describe the spread of a dataset
  • Range is a simple measure of variability, but is affected by outliers
  • Variance is the average of the squared differences from the mean, and is sensitive to units
  • Standard Deviation is the square root of the variance, and is a common measure of variability

Inferential Statistics

• Hypothesis Testing: a process to determine if a hypothesis is true or not
  • Null Hypothesis (H0) is a statement of no difference or effect, and is assumed to be true
  • Alternative Hypothesis (H1) is a statement of difference or effect, and is the hypothesis being tested
  • Test Statistic is a numerical value used to determine the significance of the results
  • P-Value is the probability of observing the test statistic assuming the null hypothesis is true, and is used to determine significance
• Confidence Intervals: a range of values within which a population parameter is likely to lie
  • Margin of Error is the maximum amount by which the sample statistic may differ from the population parameter
  • Confidence level is the probability that the interval contains the true population parameter, and is typically set to 95%

Probability

• Basic Concepts: fundamental ideas in probability theory
  • Experiment is an action or situation that can produce a set of outcomes
  • Sample Space is the set of all possible outcomes of an experiment
  • Event is a set of one or more outcomes of an experiment, and can be a subset of the sample space
• Rules of Probability: mathematical rules that govern probability
  • The probability of an event is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event
  • The probability of the sample space is 1, since it is certain to occur
  • The probability of the empty set is 0, since it cannot occur
  • The probability of the union of mutually exclusive events is the sum of their individual probabilities

Data Visualization

• Types of Plots: common types of plots used in data visualization
  • Histogram is a graphical representation of a frequency distribution, and is used to show the distribution of a single variable
  • Box Plot is a graphical representation of the distribution of a dataset, and is used to show the median, quartiles, and outliers
  • Scatter Plot is a graphical representation of the relationship between two variables, and is used to show the relationship between variables
• Data Visualization Best Practices: guidelines for creating effective visualizations
  • Clearly label axes and titles to provide context and make the visualization easy to understand
  • Use color effectively to convey information, and avoid using color unnecessarily
  • Avoid 3D plots and unnecessary embellishments, as they can be distracting and make the visualization harder to understand