Descriptive Statistics: Understanding & Calculating (AQA GCSE Psychology)

• The mean calculates the average score of a data set 
• The mean indicates what a researcher would expect to find (as the average score) if they were to replicate the procedure of a given study
• The mean is calculated using the total score of all the values in the data set divided by the number of values in that set, e.g.
  • To calculate the mean of 4, 6, 7, 9 the researcher would add up the values and then divide this total by the number of values as follows:
    
    • 4 + 6 + 7 + 9 = 26
      
    • 26 ÷ 4 = 6.5
      
    • mean = 6.5
• Advantages of using the mean
  • It is the most sensitive measure of central tendency as it takes all scores in the data set into account
  • It is more likely than other measures of central tendency to provide a representative score i.e. a reliable result  
• Disadvantages of using the mean
  • It is sensitive to extreme scores (outliers) so it can only be used when the scores are reasonably close 
  • The mean score may not be represented in the data set itself: in the example above, the mean is 6.5 which does not appear in the original data set

• The median calculates the middle value of a data set (the positional average)
• The data has to be arranged into numerical order first (with the lowest score at the beginning of the list), e.g.
  • To calculate the median of 20, 43, 56, 78, 92, 67, 48 the researcher must take the halfway point between the two middle values as the data set has an odd number of scores (7)
  • The researcher would then add the two middle values together and divide them by 2, as follows:
    • 20, 43, 56, 78, 92, 67, 48 would be ordered into 20, 43, 48, 56, 67,78, 92 = the median is the halfway point
  • If there are an even number of values we would get two values in the middle
    • In this case we take the halfway point between these two values
    • This is usually obvious but, if not, add the two middle values and divide by 2
      • This is the same as finding the mean of the middle two values 

• Advantages of using the median
• It is not affected by extreme scores
• It is easy to calculate
• Disadvantages of using the median 
• It does not necessarily represent a typical average as it does not include all of the data in its calculation i.e. it does not account for extreme scores making it less reliable than the mean
• It is impractical to use on large data sets

• The mode calculates the most frequently occurring score in a data set i.e. mode means most often
• The mode simply highlights what the most common score(s) is in a data set (some data sets will have no mode, some will have more than one)
• The mode is used when the researcher cannot use the mean or the median
• E.g. to calculate the mode of 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 7, 8 the researcher would count the number of times each score appears in the data set as follows:
• The most frequently occurring number is 6 
• The mode = 6 
• Advantages of using the mode
  • It is less likely to be affected by extreme scores
  • It is often useful for the analysis of qualitative data as this type of data may require frequencies of theme to be analysed 
• Disadvantages of using the mode
  • A data set may include two modes (bimodal) or more (multimodal) which blurs the meaning of the data
  • The mode is likely to be of little use on small data sets as it may provide an unrepresentative central measure

Calculating the mode, median and mean

• The range is a measure of dispersion
  • It calculates the spread of scores and how much they vary in terms of how distant they are from the mean or median
• A data set with low dispersion will have scores that cluster around the measure of central tendency e.g. the mean
• The range describes the difference between the lowest and the highest scores in a data set
• The range provides information as to the gap between the highest and the lowest score
• To calculate the range the researcher would subtract the lowest value from the highest value in the data set
  • E.g. to calculate the range of 4, 4, 6, 7, 9, 9 the researcher would subtract the lowest number (4) from the highest number (9) as follows:
    • 9 - 4 = 5 
    • The range = 5
• Advantages of using the range
  • It provides a broad overview of the data which can be useful for some research purposes
  • It is easy to calculate
• Disadvantages of using the range 
  • It highlights the gap between top and bottom scores but provides no information as to all of the other scores in the data set
  • It is not very stable or representative as it can vary from one sample to another as sample size increases