Presentation of quantitative data distributions

• • Normal distributions/bell shaped curve are symmetrical
  • within a normal distribution, most people are in the middle area of the curve with very few people at the extreme ends
  • the mean, median and mode all occupy the same midpoint of the curve
  • the tails of the curve, which extends outwards, never touch the horizontal x-axis are - more extreme extreme scores are always theoretically possible
• • Not all distributions form such a balanced symmetrical pattern
  • some data sets derived from psychological scales or measurements may produce skewed distributions, that is, distributions that appear to lean to one side or the other
• • A positive skew is where most of the distribution is concentrated towards the left of the graph, resulting in a long tail on the right
  • In a hypothetical test people have performed poorly
  • the mode remains at the highest point of the peak, the median comes next, but the mean is dragged across the tail
  • extreme scores affect the mean
• • the opposite occurs in a negative skew
  • a very easy test would produce a distribution where the bulk of the scores are concentrated on the right, resulting in the long tail of anomalous scores on the left
  • the mean is pulled to the left, with the mode dissecting the highest peak and the median in the middle