measures of central tendency and dispersion

• the mean is the arithmetic average. Calculate it by adding up all the scores an divide by the number of scores
• strength and limitation of mean:

  • sensitive measure- included all the scores/values in the data set within the calculation. Represents data set better than median or mode
  • may be unrepresentative- one very large or small number makes it distorted. The median or the mode tend not to be so easily distorted
• median is the middle value. Calculate by placing the score in ascending order and select middle value. If there are 2 values in the middle, the mean of these is calculated
• strength and limitation of median:

  • less affected by extreme score- the median is only focused on the middle value. In some cases may be more representative of the data set as a whole
  • less sensitive than the mean- the actual values of lower and higher numbers are ignored. Extreme values may be important
• mode is the most frequent or common. It is used with categorial/nominal data
• strength and limitation of mode:

  • relevant to categorial data- when data is discrete like represented in categories. Sometimes the mode is the only appropriate measure
  • an overly simple- the mode may be at one extreme. It is not a useful way of describing data when there are many modes
• range is the difference between the highest and lowest value
• strength and limitation of range:

  • easy to calculate- average values in order and subtract largest form smallest. Simple formula, easier than the standard deviation
  • does not count for the distribution of the scores- the range doesn't indicate whether most numbers are closely grouped around the mean or spread out evenly. The standard deviation is a much better measure of dispersion in this respect
• standard deviation is a measure of the average spread around the mean. The larger the standard deviation, the more spread out the data is
• strength and limitation of standard deviation:

  • more precise than the range- includes all values within the calculation. Therefore more accurate picture of the overall distribution of data set
  • it may be misleading- can be distorted by extreme values. Also, extreme values may not be revealed, unlike with the range
• the 3 measures of central tenancy are:

  • mean
  • mode
  • media
• the 2 measures of dispersion are:

  • range
  • standard deviation