Q6 Knowledge-Base

Crimes per Day

                                     Cumulative

  Scores   Frequency   Percent         Percent

    0          1      2.0%              2.0%

    1          2      4.1%              6.1%

    2          3      6.1%            12.2%

    3          6      12.2%            24.5%

    4          7      14.3%            38.8%

    5          7      14.3%            53.1%

    6          7      14.3%            67.3%

    7          5      10.2%            77.6%

    8          4      8.2%            85.7%

    9          3      6.1%            91.8%

    10         2      4.1%            95.9%

    11         1      2.0%            98.0%

    12         1      2.0%            100.0%

  Total       49                       100.0% 

The percentages of scores between each Z-score are not equal.. The percentages between each Z-score represent the likelihood of a person’s score falling in that range in the population. In other words, this is how the normal curve is used to compute the anterior probabilities on metric variables.

Determining Probabilities Using the Normal Curve

B.  Above: Determining the probability of finding a score above a raw score is the opposite. The percentage above a raw score can be any percentage from 1% to 99%.  A person achieving at one standard deviation above the mean is “outscored by 15.87% of the population. A person scoring at one standard deviation below the mean is “outscored” by 84.13% of the population.

 Since the percentages between each standard deviation are always constant, each standard deviation is associated with a particular percentage above:

 If Z = -2 the Percentage Above is about 98% (97.72%) 

If Z = -1 the Percentage Above is about 85% (84.13%)

If Z =  0 the Percentage Above is about 50% (50.00%)

If Z = +1 the Percentage Above is about 15% (15.87%) 

If Z = +2 the Percentage Above is about 02% (2.28%)