Statistics

• Measures of central tendency:

  • Mean
  • Median
  • Mode
• Measures of dispersion:

  • Range
  • Standard deviation
• Measures of central tendency is a single value that summarises a set of data identifying a typical value of the data set (average).
• The mode is the most frequent score in a quantitative data set. If there are two, the data is bi-modal and if there is more the two, the data is multimodal.
• Strengths of the mode:

  • Not distorted by extreme scores (outliers).
  • Helpful for more discrete numbers (eg saying a family has 2 children rather than 1.89).
  • Gives the average in categories.
• Limitations of the mode:

  • No modes if every value is different. This is usually the case in small data sets, meaning the mode does not give an exact average value.
• The median is the value in the central position of a data set.
• Strengths of the median:

  • Not affected by extreme outliers.
  • Easy to calculate.
• Limitations of the mean:

  • Does not include all values in the calculation so it is not as sensitive as the mean measure of central tendency.
  • If there are an even number of data points, the typical value will be a number that is not one of the recorded values.
• The mean is the mathematical average of a data set, calculated by adding all the values and dividing the the number of values.
• Strengths of the mean:

  • All raw data points are represented in calculating the mean. This means it is the most sensitive measure of central tendency.
• Limitations of the mean:

  • Due to the sensitivity, it is distorted by extremely high or low values (outliers).
• The range is the difference between the data sets highest and lowest values.
• Strengths of the range:

  • Easy to calculate compared to the standard deviations.
• Limitations of the range:

  • Outliers distort the value.
  • Does not show if the scores are clustered around the mean or more evenly spread out.
• The standard deviation is a complex calculation using all the data points that produces a single value. The smaller the SD the more clustered the values are around the mean.
• Strengths of the standard deviation:

  • Includes all values making it more sensitive than the range.
  • Provides information about the spread of the scores.
• Limitation of the standard deviation:

  • Extreme scores / outliers distort the SD.
  • More difficult to calculate.
• Percentage change = (new value - old value) / (old value) x 100