Measures of Central Tendency

• These measures tell us where the "middle" of the data is.
• A common word is average
  • This term has different definitions
  • The middle of a set of data: arithmetic average, median
  • The "representative" piece of data: "average man", mode
• The mean, x̄
  • x̄ = Σx/n
• The median is the middle data value.
  • Sort the data.
  • Find the middle number of the size of the data set is odd.
  • Find the average of the two middle numbers if the size of the data set is even.
• The mode is the data the occurs most frequently
  • Data sets may not have a mode, if no data occurs more than once
  • Data sets may be multimodal if several data occurs more than once and have the same maximum frequency.
  • The definition of mode sometimes excludes mutimodal data from having a mode.
• The midrange is the average of the maximum and minimum data values.
• Do some problems 803.

Measures of Position

• These measures tell the location of a piece of data within the entire data set.
• This is useful when you wish to compare one piece of data to the rest of the data.
• The easiest is to determine if the item is in the upper or lower half of the data.
  • Compute the median.
  • If the data is larger than the median it is in the top 50% , otherwise it is in the lower 50%.
  • This means 1/2 either did better or worse.
• Quartiles refine this
  • 4 bins not 2.
  • Compute the median.
  • Divide the data into two sets based on the median.
    • If there is an odd number of data, exclude the median from either set
    • Compute the median of each data set.
• Percentiles take this even further, 100 bins, not 4.
• Do problems 48 and 50 page 805.