reading 3

• What do measures of central tendency identify?

  The center or average of a dataset
• What is the arithmetic mean?

  Sum of values divided by number of observations
• What is a sample mean?

  Sum of sample values divided by sample size
• Why is the sample mean used?

  To make inferences about the population mean
• What is the median?

  The midpoint of a dataset
• How is the median determined?

  By arranging data and finding the middle observation
• Why is the median important?

  It is not affected by outliers
• What is the median return for the dataset: 30%, 15%, 25%, 21%, 23%?


  23%
• How do you find the median with an even number of observations?

  Calculate the mean of the two middle values
• What is the mode?

  The value that occurs most frequently
• Can a dataset have more than one mode?

  Yes, it can be unimodal, bimodal, or trimodal
• What is the mode of the dataset: [30%, 28%, 25%, 23%, 28%, 15%, 5%]?

  28%
• How do we handle modes in continuous data?

  Identify the modal interval with the most observations
• What is a trimmed mean?

  A mean excluding extreme observations
• What is a winsorized mean?

  A mean with extreme values substituted
• What is a quantile?

  A value below which a proportion of data lies
• What is a quartile?

  A division of data into four equal parts
• What is the interquartile range?

  The difference between the third and first quartiles
• What does a box and whisker plot represent?

  Visualizes data based on quantiles
• What is dispersion?

  Variability around the central tendency
• What is the formula for range?

  Range = maximum value - minimum value
• What is the range for returns: 30%, 12%, 25%, 20%, 23%?

  18%
• What is the mean absolute deviation (MAD)?

  Average of absolute deviations from the mean
• What does a MAD of ±4.8% indicate?

  Individual returns deviate from the mean
• What is sample variance?

  Measure of dispersion for a sample of observations
• Why do we use n - 1 in sample variance calculation?

  To avoid underestimating population variance
• What is the problem with using variance?

  It is difficult to interpret squared units
• What is the sample standard deviation?

  Square root of the sample variance
• What does a sample standard deviation of ±6.67% indicate?

  Individual returns deviate from the mean
• What is the coefficient of variation (CV)?

  Measure of dispersion relative to the mean
• How is CV calculated?

  CV = standard deviation / mean
• What does a lower CV indicate?

  Less risk per unit of expected return
• What does a higher CV indicate?

  More risk per unit of expected return
• Why is the dispersion of two distributions not meaningful when their means differ significantly?

  A relative measure of dispersion must be used
• What is relative dispersion?

  Variability around a reference point
• How is relative dispersion commonly measured?

  With the coefficient of variation (CV)
• What does the coefficient of variation (CV) measure?

  Dispersion relative to the distribution's mean
• In an investment context, what does a lower CV indicate?

  Less risk per unit of expected return
• What is target downside deviation?

  A measure of risk considering only outcomes below a target
• How is target downside deviation calculated?

  Using deviations from a target value