Data Analysis: Descriptive Statistics

• Measures of Central Tendency


  Measures of central tendency are 'averages' we use them to find the most typical values in a set of data.
• Mean


  Add all the data and divide by however many data values there are.
• When should I use the mean?

  When there are no extreme data scores.
• Strengths and limitations of mean

  +It is the most sensitive of all this measures of central tendency as it includes all scores.

  -It is easily distorted by extreme values, it stops the mean representing the whole data.
• Median


  Put all data values in order of lowest to highest then find the one in the middle. If you have an even number of scores in a data set, put all data values in order of lowest to highest then find the one in the middle. If you have an even number of scores in a data set then the median is halfway between the two middle scores.
• When should I use the median?

  When there are extreme data scores in the data set
• Median strengths and limitations

  +Not affected by extreme scores so the average is more realistic

  -Less sensitive then the mean as not all scores are included
• Mode


  The most commonly occurring data score in the data set. There may be 2 modes (bimodal) or no mode at alll.
• When should I use the mode?

  When data is categorical.
• Strengths and limitations of mode

  +Shows the most common category in nominal data

  -Less sensitive than the mean as only a couple of values may be used

  -Not unique as there is likely to be more than one mode
• Measures of dispersion


  Based on the spread of scores; that is, how far scores vary and differ from each other.
• Range


  You need to be able to work out the range.

  Take the smallest value from the largest value, and add 1

  e.g. the scores on a maths test out of 20

  16 9 4 19 15 7 10 12

  the range would be (19 - 4) + 1 = 16

  +Easy to calculate

  -Only takes into account 2 most extreme values so isn't representative
• Standard deviation


  You don't need to work out standard deviation

  + More precise as it encompasses all values

  -Swayed by extreme results