DESCRIPTIVE STATS AND GRAPHS

• Mean – the arithmetic average calculated by adding up all the values in a data set and dividing by the number of values there are. 
• Mean

  Strength: includes all scores – most representative 

  Limitation: easily distorted by extreme values 
• Mode – the most frequently occurring value in a set of data. In some data, there may be two modes (bimodal) or no modes if all the scores are different (must use this for data in categories) 
• Mode

  Strength: easy to calculate  

  Limitation: not very representative of the whole data set 
• Median – the central value in a set of data when values are arranged from lowest to highest 
• Median

  Strength: not affected by extreme scores and easy to calculate 

  Limitation: doesn’t use all the data in the set – lower and higher numbers may be ignored 
• Measures of central tendency

  1. Mean
  2. Mode
  3. Median
• Measures of dispersion

  1. Range
  2. Standard deviation
• Range – calculated by subtracting the lowest score from the highest score and adding one as a mathematical correction 
• Range

  Strength: easy to calculate 

  Limitation: only considers the two most extreme scores – unrepresentative 
• Standard deviation – a measure of dispersion (spread) in a set of scores. It tells us how much scores deviate from the mean by calculating the difference between the mean and each score. All the differences are added up and divided by the number of scores. This gives the variance. The standard deviation is the square root of the variance. This is a single value. The larger the standard deviation, the greater the dispersion (spread) of scores. A low standard deviation indicates that all respondents answered in a similar way. 
• Standard deviation

  Strength: precise as it includes all the values in the calculation 

  Limitation: can be distorted by extreme values. 
• How to interpret standard deviation

  The higher the value (e.g. SD=4) = greater spread of data = participants responded to IV differently 

  The lower the value (e.g. SD=1) = data is tightly clustered around mean = participants responded in a similar way to each other 
• Tables, graphs and scattergrams: 

  1. Summary table
  2. Bar chart
  3. Histogram
  4. Scattergram
• Summary table


  Includes measures of central tendency, measures of dispersion and provides a clear summary of data 
• Bar chart

  • Used to represent ‘discrete data’ where the data is in separate categories, which are placed on the x-axis 
  • The mean or frequency is on the y-axis 
  • Columns do not touch and have equal width a spacing 
  • Examples: differences in males/females on a spatial task or score on a depression scale before and after treatment 
• Histogram

  • Used to represent data on a ‘continuous’ scale 
  • Columns touch because each one forms a single score (interval) on a related scale e.g. time – number of hours of homework students do each week 
  • Scores (intervals) are placed on the x-axis 
  • The height of the column shows the frequency of values e.g. number of students in each interval – on the y-axis 
• Scattergram

  • Used for measuring the relationship between two variables  
  • Data from one variable is presented on the x-axis, while the other is presented on the y-axis 
  • We plot an ‘x’ on the graph where the two variables meet 
  • The pattern of plotted points reveals different types of correlation – positive, negative or none 
• Types of distribution/distribution curves


  Normal distribution

  Skewed distribution
• Normal distribution

  • This is symmetrical, producing a bell-shaped curve. 
  • The mean, mode and median are all at the same point, with very few people are the extreme ends. 
• Skewed distribution

  • A spread of frequency data that is not symmetrical, where the data is clustered on one end. 
  • Positively skewed distribution – most of the distribution is concentrated towards the left – could be because of a difficult test with low scores – the mean is greater than the median and mode 
  • Negatively skewed distribution – most of the distribution is concentrated towards the right – easy test with mostly high scores – the mean is less than the median and mode