Data analysis: Descriptive statistics

• Descriptive statistics are used to identify trends and analyse sets of data.

  • They do not allow conclusions about cause and effect, but give an overview of what the data looks like.
• Measures of central tendency are 'averages' which describe the typical value in a data set. These include the mean, median and mode.
• Mean (average)

  • Add up all the values and divide by the number of values.
  • ✅ Advantage: Uses all values in the data set → sensitive and more representative of the data.
  • ❌ Disadvantage: Affected by extreme values (outliers).
• Median

  • The middle value when scores are ranked in order.
  • For even numbers, take the average of the middle two.
  • ✅ Not affected by extreme scores.
  • ❌ Doesn’t consider all values → less sensitive and representative of the data.
• Mode

  • The most frequent value in a set.
  • ✅ Can be used with nominal data.
  • ❌ May not be representative, especially if multiple modes (bimodal/multimodal) or no mode.
• Measures of dispersion measure the spread of data. These include the range and standard deviation.
• Range

  • Highest – Lowest value
  • Often presented with +1 to account for rounding errors.
  • ✅ Easy to calculate.
  • ❌ Affected by extreme values → so may be unrepresentative of the data.
• Standard Deviation (SD)

  • Shows how far scores deviate from the mean.
  • Larger SD = more spread out.
  • ✅ More precise than the range, uses all data.
  • ❌ More complex to calculate, influenced by outliers.
• If there are no outliers, the best measure of central tendency to use is the mean, and the best measure of dispersion is the standard deviation.
• If there are outliers present in the data, the best measure of central tendency is the median, and the best measure of dispersion is the range.
• If the data is nominal, the best measure of central tendency to use is the mode.