Research

• Measures of Central Tendency


  A measure of central tendency is a descriptive statistic that describes the average, or typical value of a set of scores
• Common measures of central tendency


  • The mode
  • The median
  • The mean
• Mode


  The score that occurs most frequently in a set of data
• Bimodal distribution


  A distribution that has two "modes"
• Multimodal distribution


  A distribution that has more than 2 "modes"
• When to use the mode


  • It is insensitive to large changes in the data set
  • Two data sets that are very different from each other can have the same mode
• Median


  The 50th percentile, the score in the middle; half of the scores are larger than the median and half of the scores are smaller than the median
• How to calculate the median

  1. Sort the data from highest to lowest

  2. Find the score in the middle

  3. middle = (N + 1) / 2

  4. If N is even, the median is the average of the middle two scores
• When to use the median


  • Often used when the distribution of scores is either positively or negatively skewed
• Mean


  • The arithmetic average of all the scores
  • The number that makes the sum of the deviations from it equal to 0
  • The number that makes the sum of the squared deviations a minimum
• Calculating the mean


  1. Sum the scores (X)

  2. Divide the sum (X) by the number of scores (N)
• When to use the mean


  • When the data are interval or ratio scaled
  • Many people will use the mean with ordinally scaled data too
  • When the data are not skewed
• In symmetrical distributions


  The median and mean are equal
• For normal distributions


  Mean = median = mode
• In positively skewed distributions


  The mean is greater than the median
• In negatively skewed distributions


  The mean is smaller than the median