Descriptive Statistics Quiz

Descriptive Statistics

• Measures that summarize and describe the basic features of a dataset
• Types:
  • Measures of central tendency:
    • Mean (average value)
    • Median (middle value)
    • Mode (most frequent value)
  • Measures of variability:
    • Range (difference between largest and smallest values)
    • Interquartile range (IQR, difference between Q3 and Q1)
    • Variance (average of squared differences from the mean)
    • Standard deviation (square root of variance)

Inferential Statistics

• Uses sample data to make inferences about a population
• Types:
  • Estimation:
    • Point estimation (single value estimate of a population parameter)
    • Interval estimation (range of values within which a population parameter is likely to lie)
  • Hypothesis testing:
    • Null hypothesis (H0, a statement of no difference or effect)
    • Alternative hypothesis (H1, a statement of difference or effect)
    • Test statistic (a value calculated from sample data to test H0)
    • P-value (probability of observing the test statistic by chance)

Probability

• The study of chance events and their likelihood of occurrence
• Key concepts:
  • Event: a set of outcomes of an experiment
  • Sample space: the set of all possible outcomes of an experiment
  • Probability of an event: a number between 0 and 1 that represents the likelihood of the event occurring
  • Conditional probability: the probability of an event occurring given that another event has occurred
  • Independence: two events are independent if the occurrence of one does not affect the probability of the other

Data Visualization

• The use of graphical representations to communicate information about data
• Types of plots:
  • Histograms: show the distribution of a single variable
  • Bar charts: compare categorical data across different groups
  • Scatter plots: show the relationship between two continuous variables
  • Box plots: show the distribution of a single variable and compare across different groups

Descriptive Statistics

• Summarize and describe the basic features of a dataset
• Central tendency measures:
  • Mean: average value of a dataset
  • Median: middle value of a dataset when arranged in order
  • Mode: most frequent value in a dataset
• Variability measures:
  • Range: difference between largest and smallest values in a dataset
  • Interquartile range (IQR): difference between Q3 (75th percentile) and Q1 (25th percentile)
  • Variance: average of squared differences from the mean
  • Standard deviation: square root of variance, measures spread of data

Inferential Statistics

• Uses sample data to make inferences about a population
• Estimation:
  • Point estimation: single value estimate of a population parameter
  • Interval estimation: range of values within which a population parameter is likely to lie
• Hypothesis testing:
  • Null hypothesis (H0): statement of no difference or effect
  • Alternative hypothesis (H1): statement of difference or effect
  • Test statistic: value calculated from sample data to test H0
  • P-value: probability of observing the test statistic by chance

Probability

• Study of chance events and their likelihood of occurrence
• Event: set of outcomes of an experiment
• Sample space: set of all possible outcomes of an experiment
• Probability of an event: number between 0 and 1 representing likelihood of event occurring
• Conditional probability: probability of an event occurring given that another event has occurred
• Independence: two events are independent if occurrence of one does not affect probability of the other

Data Visualization

• Use of graphical representations to communicate information about data
• Types of plots:
  • Histograms: show distribution of a single variable
  • Bar charts: compare categorical data across different groups
  • Scatter plots: show relationship between two continuous variables
  • Box plots: show distribution of a single variable and compare across different groups