Remediation 6.1 CFA Empirical Rule & Z-Score

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We are going to dive into "Normal" Shapes and what makes data normal

Empirical Rule

​68%

​According to the definition above this picture, 68% of our data falls within one standard deviation (jump) from the mean. This, inturn, means each section is worth 34% & 34%

34

34

95%

​According to the definition above this picture, 95% of our data falls within two standard deviations (jumps) from the mean. This, inturn, means the next two sections are worth 13.5% & 13.5%

34

34

13.5

13.5

99.7%

​According to the definition above this picture, 99.7% of our data falls within three standard deviations (jumps) from the mean. This, inturn, means the next two sections are worth 2.35% & 2.35%

34

34

13.5

13.5

2.35

2.35

​According to the definition above this picture, our whole curve is worth 100%. This, inturn, means the very last two sections are worth .15% & .15%
Adding ALL of these percents up means the curve adds up to 100%

34

34

13.5

13.5

2.35

2.35

.15

.15

• In order to compare different data sets we "standardize" the data so that is can be easily compared.

• Z-scores of data sets can be compared to other data sets.

• They tell you how many Standard Deviations above or below the mean the given data point lies.

• Positive z - The point is above the Mean

• Negative z - The point is below the Mean

• z is 0 - The point is the same as the mean.