By Alvan R Feinstein

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Instead, the curve of relative frequencies is “monotonic,” continuously rising toward (or falling from) a crest that occurs at one end of the distribution. One type of sloping distribution is sometimes called J-shaped; another type is called inverse-J-shaped, or L-shaped. Statisticians often use the word exponential for these sloping shapes. Shapes can also be described as centripetal if their crest (or crests) are somewhere near the center of the distribution away from either end. All basically convex shapes are centripetal.

A symmetrical distribution need not be convex. Symmetrical shapes can also be produced by abimodal distribution with two distinctive crests and by a concave distribution with a U-shaped trough. ) Bimodal and concave distributions can also be asymmetrical, according to the location of the crests and troughs. A sloping distribution does not have the fall-rise-fall or rise-fall-rise pattern of any of the previous shapes. Instead, the curve of relative frequencies is “monotonic,” continuously rising toward (or falling from) a crest that occurs at one end of the distribution.

In strict mathematical usage, the Σ is accompanied by upper and lower symbols that indicate exactly where the summation begins and ends. For the complete c . In pragmatic usage, however, the sum collection of data, the result here would be shown as N = iΣn i =1 almost always extends from the first to the last items. ] The actual frequencies are converted to relative frequencies when cited as proportions of the total group. Thus, the relative proportion of the ith category is pi = ni/N. 09 or 9%.