Empirical Rule Lesson

Empirical Rule
(68-95-99.7 Rule)

You will be filling in your notes in your packet, so please have that out as you go through this powerpoint.

Turn to this page in your notes, first!

​

Shapes

This distribution is "Skewed Right"

(The tail is on the right)

There is a lot of low numbers, and not a lot of high numbers.

​Examples:
# of siblings people have
# of pets people have

This distribution is "Symmetrical"
or
"Normal"

There is a lot of average/middle values

​​Examples:
IQ level
PSAT Scores

This distribution is "Skewed Left"

(The tail is on the left)

There is a lot of high numbers, and not a lot of
low numbers.

​​​Examples:
Grades on an easy test

Multiple Choice

How would you describe this data?

• Skewed Left

• Skewed Right

• Symmetrical

Multiple Choice

Describe the data distribution shape of the graph.

• Skewed right
• Skewed left
• Symmetrical

Multiple Choice

How would you describe this distribution?

• Left skewed
• Right Skewed
• Symmetrical

Multiple Choice

What is the shape of the distribution?

• Skewed Left

• Skewed Right

• Symmetrical

Multiple Choice

What is the shape of the distribution?

• Skewed left

• Skewed right

• Symmetrical

Multiple Choice

This data is

• symmetrical

• skewed right

• skewed left

Turn to this page in your notes!

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

Empirical Rule

Fill in the blanks!

​68%

1

​95%

2

3

​99.7%

The mean is always in the middle of our picture/distribution. Then we use the standard deviations to "jump" from value to value.

What does this mean?

Turn to this page in your notes!

Empirical Rule

(step 1)
Focus on the tick marks on the bottom of the curve

(step 2)
Write the mean (from the problem) in the middle

​70

(step 3)
Find the standard deviation (in the problem) is 5

(step 4)
Count by 5's along the bottom line (each tick mark)

​70

​75

80

85

65

60

55

Flip back to this page :)

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

Flip back to this page!

Empirical Rule

The percents are the SAME exact percents EVERY time. So we can use the percents from the previous slides to fill in these gaps...
click next to see this!

​70

​75

80

85

65

60

55

We need to put these percentages here before each problem.

​70

​75

80

85

65

60

55

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

​70

​75

80

85

65

60

55

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

​To answer this question, add up the percents that are between the values of 65 and 75 on our number line!

​70

​75

80

85

65

60

55

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

Answer: 34% + 34% = 68%

​70

​75

80

85

65

60

55

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

Answer: 13.5%

​70

​75

80

85

65

60

55

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

Answer: 13.5% + 34% = 47.5%

​70

​75

80

85

65

60

55

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

Answer: .15%

​24

28

32

36

20

16

12

Example 2 - Step 1 - Find mean and standard deviation and label the curve

24

28

32

36

20

16

12

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

Example 2 - Step 2 - Fill in percents

24

28

32

36

20

16

12

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

Answer: 13.5% + 34% + 34% + 13.5% = 95%

24

28

32

36

20

16

12

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

Answer: 2.35%

24

28

32

36

20

16

12

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

Answer: 13.5% + 2.35% = 15.85%

24

28

32

36

20

16

12

34%

34%

13.5%

13.5%

2.35%

2.35%

.15%

.15%

Answer: 34% + 13.5% + 2.35% + .15% = 50%

Complete the 6 questions
on DeltaMath to finish and
practice this material