Measures of Central Tendency & Dispersion

• What are the measures of central tendency?

  Mean, Median, Mode
• What is the mean?

  The average of all values in data
• What is a strength of the mean?

  It includes all values in the calculation
• What is a limitation of the mean?

  It can be distorted by extreme values
• What is the median?

  The central value in arranged data
• What is a strength of the median?

  It is not distorted by extreme values
• What is a limitation of the median?

  It is less sensitive than the mean
• What is the mode?

  The most frequently occurring value
• What is a strength of the mode?

  It is unaffected by extreme values
• What is a limitation of the mode?

  Not useful with several modes present
• What are the measures of dispersion?

  Range, Standard Deviation
• What is the range?

  Difference between highest and lowest values
• What is a strength of the range?

  It is easy to calculate
• What is a limitation of the range?

  It is affected by extreme values
• What is the standard deviation?

  Measure of average deviation from the mean
• What is the formula for standard deviation?

  $\sigma =$$\sqrt{\frac{\sum(value (X) - mean (X̄))^2}{total value (n)}}$
• What is a strength of the standard deviation?

  It includes all values for precision
• What are the strengths and limitations of the mean?

  Strengths:

  • Most sensitive measure
  • More representative of data

  
  

  Limitations:

  • Distorted by extreme values
  • Can misrepresent overall data
• What are the strengths and limitations of the median?

  Strengths:

  • Not distorted by extremes

  
  

  Limitations:

  • Less sensitive than the mean
  • Not all scores included
• What are the strengths and limitations of the mode?

  Strengths:

  • Unaffected by extremes
  • Useful for categorical data

  
  

  Limitations:

  • Not useful with several modes
• What are the strengths and limitations of the range?

  Strengths:

  • Easy to calculate

  
  

  Limitations:

  • Affected by extreme values
  • Ignores distribution of numbers
• What are the strengths and limitations of the standard deviation?

  Strengths:

  • More precise measure of dispersion

  
  

  Limitations:

  • More complex to calculate