Summary of Measures

• What is the purpose of compressing mass data in measures?

  To achieve better comprehension and description
• What are the categories of measures summarized in the study material?

  • Measures of central tendency
  • Measures of dispersion
  • Measures of location
• What does the term "measures of central tendency" refer to?

  It refers to the "center" of the distribution of observations
• What are the most common measures of central tendency?

  • Mean
  • Median
  • Mode
• What is the arithmetic mean also known as?

  Average
• How is the mean computed?

  By summing all observations and dividing by the number of observations
• Why is the mean sensitive to extreme observations?

  Because it involves all observations in its computation
• What happens to the mean if any observation changes?

  Any change in the observation will change the mean value
• For what type of variable can the mean be calculated?

  Any quantitative variable
• What is the unit of the mean?

  The same as that of the original set of observations
• What does the sum of the deviations of the observations from the mean equal?

  Zero
• What does the mean represent in a distribution?

  It serves as the point of balance or center of gravity of the distribution
• Why is the mean important in statistics?

  It serves as the basis for the computation of higher statistical methods
• What is the median?

  The middle most value in a set of observations put in an array
• How is the median determined if the number of observations is odd?

  It is the middle most observation
• How is the median determined if the number of observations is even?

  It is the mean of the three middlemost observations
• How can the position of the median be computed?


  As $\frac{n + 1}{2}$
• What is a key characteristic of the median?

  It always exists and is unique
• How does the median respond to outliers?

  It is not influenced by outliers
• What observations does the median use in its computation?

  It does not make use of all the observations
• For what types of variables can the median be calculated?

  Any quantitative variable and some qualitative variables
• What is the mode?

  The most frequently occurring value in a set of observations
• What are the possible scenarios regarding the mode in a dataset?

  There can be no mode, unimodal, bimodal, or multimodal
• What calculations are needed to determine the mode?

  No calculations are needed
• For what types of variables can the mode be determined?

  Any type of variable
• What are measures of dispersion used for?

  • To give information about the tendency of values to clump together
  • To describe the variability of the observations
  • Applicable only for quantitative variables
• What are the most common measures of dispersion?

  • Range
  • Variance
  • Standard deviation
  • Coefficient of variation
• What is the range?

  The simplest measure of location
• How is the range calculated?

  By subtracting the lowest observation from the highest observation
• What does the range not provide information about?

  It does not tell anything about the observations between the two extreme observations
• For what type of variables can the range be used?

  Quantitative variables only
• What is variance?

  A measure of variability that takes the mean as the reference point
• How is variance calculated?

  By taking the mean as the reference point and involving all observations
• What is the unit of variance?

  Squared unit of the original set of observations
• Why is variance hard to interpret?

  Because it is expressed in squared units
• What is standard deviation?

  The square root of variance
• What is the unit of standard deviation?

  The same as that of the original set of observations
• How is the coefficient of variation expressed?

  As a percentage of the mean
• When is the coefficient of variation most appropriate to use?

  When the unit of measurement of variables being compared are different
• What does a low coefficient of variation indicate?

  A low measure of dispersion