Distribution Shapes (STATS&PROBABILITY)

• Distributions are most often not perfectly shaped, so it is not

  necessary to have an exact shape but rather to identify an overall

  pattern.
• A bell-shaped distribution shown above has a single peak and

  tapers off at either end. It is approximately symmetric; i.e., it is

  roughly the same on both sides of a line running through the

  center.

  
• A uniform distribution is basically flat or rectangular.

  
• A J-shaped distribution is shown above, and it has a few data

  values on the left side and increases as one moves to the right.

  
• When a distribution has two peaks of the (almost) the same height, it is said to be bimodal.

  
• A U-Shaped distribution is a graphical representation of a

  frequency distribution that is shaped more or less like the letter

  U, with the maximum frequencies at both ends of the range of

  the variable.

  
• When the peak of a distribution is to the left and the data values taper off to the right, a distribution is said to be positively or right-

  skewed.

  
• When the data values are clustered to the right and taper off to

  the left, a distribution is said to be negatively or left-skewed.

  
• If the mean, median, and mode are not at the same point, then

  the frequency distribution is asymmetrical.
• Skewness (SK) is the degree of departure from the symmetry or

  asymmetry of a distribution.