and the 68-95-99.7 Rule

THE NORMAL DISTRIBUTION

SKEWED DISTRIBUTIONS & OUTLIERS

NORMAL = TYPICAL• This is valuable information when studying

human behavior • i.e., the average woman is 5’4” tall (64 inches) …

this means that we expect to see women of this height. It is uncommon to see women who are 6 feet tall or 4 feet tall.

• i.e., the average intelligence score is 100…it is rare to score 130 or 70.

• Standard Deviation

• Range

• Mean

• Median

• Mode

DESCRIBING ‘NORMAL’ W/ STATSCENTRAL TENDENCY VARIATION

IN ORDER TO INTERPRET THE NORMAL CURVE BOTH PIECES OF INFORMATION ARE NECESSARY.

WHY?

• Did everyone get a 30?

• Did half of the students get a 20 and the other half get a 40?

• Was my score good or bad?

I.E., THE AVERAGE SCORE ON THE QUIZ WAS 50 POINTS…

• We know how spread out the grades are but not how they are centered

• How did the class do in general?

• Is my grade good or bad?

I.E., THE SD ON THE QUIZ WAS 5

• Allows us to make accurate assumptions and inferences about data on a normal curve

68-95-99.7 RULE

68% OF ALL DATA WILL FALL WITHIN ONE STANDARD DEVIATION OF THE MEAN.

95% OF ALL DATA WILL FALL WITHIN TWO STANDARD DEVIATIONS OF THE MEAN.

99.7% OF ALL DATA WILL FALL WITHIN THREE STANDARD DEVIATIONS OF THE MEAN.

QUIZ EXAMPLE…M=50 AND SD=5• Now we know that 68% of students scored between 45

and 55

• 95% of students scored between 40 and 60

• 99.7% of students scored between 35 and 65

Height example…M=64, SD=3So…68% of all women are within 3 inches of 64.68% of all women are within 1 standard deviation of the mean.

95% of all women are within 2 standard deviations of the mean.Here 95% of all women are within 6 inches of 64.

99.7% of all women are within 3 standard deviations of the mean.Here 99.7% of all women are within 9 in. of 64.

PRACTICE PROBLEMS

• The average height at TCC is 66 inches with a standard deviation of 4.5 inches. Display this information on a normal curve.

• How tall is someone 2 standard deviations above the mean?

• Answer: 66+4.5+4.5=75 inches • What percentage of students are between

61.5 and 70.5 inches?• Answer: 68%

• What percentage of students are below 70.5?

• Answer: 84%• 50%+34%=84%

• What percentage of students are below 75?

• Answer: 97.5

• What percentage of students are above 79.5?

• Answer: 0.15%