Measures of central tendency and dispersion

• what are the three measures of central tendency?

  mean, median and mode.
• what are the two measures of dispersion

  range, standard deviation.
• mean 


  arithmetic average, add up all the scores and divide by the number of scores.
• strength of the mean

  sensitive. includes all the scores in the data set within the calculation. more of an overall impression of the average than median or mode.
• limitation of the mean

  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


  middle value, place scores in ascending order and select middle value. if there are two values in the middle, the mean of these is calculated.
• strength of the median

  unaffected by extreme scores. the median is only focused on the middle value. it may be more representative of the data set as a whole.
• limitation of the median


  less sensitive than the mean. not all scores are included in the calculation of the median. extreme values may be important.
• mode


  most frequent or common value, used with categorical/nominal data.
• strength of the mode

  relevant to categorical data. when data is 'discrete', i.e. represented in categories. sometimes, the mode is the only appropriate measure.
• limitation of the mode

  an overly simple measure. there may be many modes in a data set. it is not a useful way of describing data when there are many modes.
• range


  the difference between the highest to lowest value.
• strength of the range

  easy to calculate. arrange values in order and subtract smallest from largest. simple formula, easier than the standard deviation.
• limitation of the range

  doesn't account 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


  measure of all the average spread around the mean. the larger the standard deviation, the more spread out the data are
• strength of standard deviation

  more precise than the range. includes all values within the calculation. a more accurate picture of the overall distribution of the data set.
• limitation of standard deviation

  it may be misleading. may 'hide' some of the characteristics of the data set. extreme values may not be revealed, unlike with the range.