Properties of a normal statistical curve

• The normal distribution is a widely used statistical tool.


• The normal distribution is often referred to as a bell curve, given its bell-type shape and perfect symmetry.


• The normal curve represents a distribution of individuals and generally indicates that most individuals are typical or normal on a particular measurement, but some individuals differ from that norm; as one moves further and further away from the center of the normal curve, individuals tend to exhibit characteristics that are more atypical of the norm.


• A curious thing happens when data is summarized in a frequency distribution polygon. Regardless of the characteristics being measured (e.g., achievement, personality, height e.t.c.,) often this frequency polygon looks like a bell and so it is described as a bell-shaped curve.


• The curve is roughly symmetric, with the most frequently earned scores at the middle of the distribution and the least earned scores at the extreme of the distribution.


• The mean, mode and median provide about the same numerical values as
measures of central tendency of this distribution.

• However, a normal distribution is a mathematical idealization of a particular type of symmetrical distribution; but it is a good mathematical curve that provides a good model of relative frequency distribution found in behavioral research.


• Therefore, the normal curve is the most important of all frequency polygons because any data from any variable describes a normal curve e.g., height, weight…, the normal curve is also a useful with inferential statistics as a probability distribution.


Properties of the Normal Distribution



  1. Unimodal (one mode) – this implies that in a large frequency distribution then most frequently observed score X, is that value of X falling exactly at the mean of the distribution. The greater the distance between X and the mean, the smaller the frequency with which X occurs; hence the characteristic of the bell shaped.
  2. Symmetrical (left and right halves are mirror images)– just as many people above the mean as below the mean. If the normal curve is folded about its mean, the two halves will be mirror images of each other. Therefore, the percentage of scores above the mean equals the percentage of scores below the mean.
  3. Bell shaped (maximum height (mode) at the mean) Mean, Mode, and Median are all located in the center-they are equal.
  4. Asymptotic (the further the curve goes from the mean, the closer it gets to the X axis; but the curve never touches the X axis) –the normal curve is continuous for all values of X from -∞ to +∞ ; but never touches the abscissa.