Distributions:

• Background on distributions:

  • When we plot continuous data, the overall pattern of the plotted data is collected is called a distribution
  • A distribution can be normal or skewed
• Normal distribution:

  • A normal distribution has certain defining features:
  • The mean, median and mode are all in the exact same mid-point
  • The distribution is symmetrical around this mid-point
  • The dispersion of values either side of the mid-point is consistent and can be expressed in standard deviations
• In any normal distribution:

  • 68% of values lie within 1 standard deviation of the mean
  • 95% of values lie within 2 standard deviations of the mean
  • 99.7% of values lie within 3 standard deviations of the mean
• Skewed distribution:

  • A skewed distribution is when values are not distributed symmetrically around the mean
• What is a positive skew?

  • A positive skew is where most of the distribution is concentrated towards the left of the graph
  • There is a tail to the right of the graph
  • The mode remains at the highest point of the peak, the median comes next, but the mean has been dragged across to the right because it has been affected by the extreme values
  • A positive skew would be produced by a very difficult test in which most participants got a low score
• What is a negative skew?

  • A negative skew is where most of the distribution is concentrated towards the right of the graph
  • There is a tail to the left of the graph
  • The mode remains at the highest point of the peak, the median comes next, but the mean has been dragged across to the left because it has been affected by extreme values
  • A negative skew would be produced by a very easy test in which most participants got a high score