Distributions

• IQ test


  A series of logic questions that results in a score, a measure of intelligence
• Average IQ score


  • 100
  • Most people score close to 100
  • Very few have exceptionally high or low scores
• Normal distribution


  A bell-shaped curve that is a common distribution of data
• Normal distribution


  • Symmetrical on both sides
  • Mean, median and mode are at the top in the center
  • Sides don't touch the x-axis
• The mode is the most common or frequent score
• The median is the middle score
• The mean is kept in the center as the extreme scores on each side balance out
• Standard deviation


  • Measure of how far a score is from the mean
  • 68% of scores are within 1 standard deviation
  • 95% are within 2 standard deviations
  • 99.7% are within 3 standard deviations
• A score of 130 on an IQ test is in the top 2.5% of the population, as it is 2 standard deviations from the mean
• Positive skew


  Distribution with a long tail pointing to the right
• Negative skew


  Distribution with a long tail pointing to the left
• Easy test questions


  Negative skew distribution with most scores high
• Difficult test questions


  Positive skew distribution with most scores low
• In a skewed distribution, the mode is the highest point, the mean is pulled towards the tail, and the median is between the mode and the mean