Remediation 6.1 CFA Empirical Rule & Z-Score

Empirical Rule
(68-95-99.7 Rule)

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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

Multiple Choice

What percent of people within 1 standard deviation of the mean?

• 99.7

• 34

• 68

• 95

Multiple Choice

What percent of people within 2 standard deviations of the mean?

• 99.7

• 34

• 68

• 95

Multiple Choice

What percent of people within 3 standard deviations of the mean?

• 99.7

• 34

• 68

• 95

Multiple Choice

Which interval shows 68% of the data given a mean of 15 and a standard deviation of 3? 

• 9 to 21

• 12 to 18

• 6 to 24

• 13 to 16

Multiple Choice

Which interval shows 95% of the data given a mean of 15 and a standard deviation of 3? 

• 9 to 21

• 12 to 18

• 6 to 24

• 13 to 16

Multiple Choice

Which interval shows 99.7% of the data given a mean of 15 and a standard deviation of 3?

• 9 to 21

• 12 to 18

• 6 to 24

• 13 to 16

What is a z-score and Why do we use it?

• 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.

Multiple Choice

In the formula for z-score what does the x stand for?

• the data point in question

• the mean of the data set

• the standard deviation of the data set

• the mode

Multiple Choice

In the formula for z-score what does the symbol below stand for?

$$\mu$$  

• the data point in question

• the mean of the data set

• the standard deviation of the data set

• the mode

Multiple Choice

In the formula for z-score what does the symbol below stand for?

$$\sigma$$  

• the data point in question

• the mean of the data set

• the standard deviation of the data set

• the mode

Z- SCORES

• 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.

Multiple Choice

If the z - score is 1.5 the data point ________ the mean.

• above

• below

• the same as the mean

Multiple Choice

If the z - score is -1.5 the data point ________ the mean.

• above

• below

• the same as the mean

Multiple Choice

Find the Z-score.

Mean = 22

Standard Deviation: 3.1

x = 29

• 2.26

• 16.45

• -2.26

• 1.26

Multiple Choice

Find the Z-score.

Mean = 21

Standard Deviation: 1.3

x = 22

• 0.77

• 5.33

• 1.07

• 1.26

Multiple Choice

Find the Z-score.

Mean = 27

Standard Deviation: 1.4

x = 11

• -11.43

• 7.85

• -2.33

• 4.16