Understanding the Empirical Rule

This video tutorial explains the empirical rule for normal distributions, which helps determine the percentage of data within one, two, or three standard deviations from the mean. The rule states that 68% of data falls within one standard deviation, 95% within two, and 99.7% within three. The video includes examples using exam grades and women's heights to illustrate the application of the rule. It concludes with a brief summary and directs viewers to additional resources for further learning.

What is the empirical rule used for?

• To calculate the mode of a dataset

• To determine the mean of a dataset

• To find the median of a dataset

• To estimate the percentage of data within certain standard deviations of the mean

According to the empirical rule, what percentage of data lies within one standard deviation of the mean?

• 68%

• 50%

• 95%

• 99.7%

What percentage of data is expected to be within two standard deviations of the mean?

• 99.7%

• 100%

• 95%

• 68%

How much data is expected to be within three standard deviations of the mean according to the empirical rule?

• 100%

• 99.7%

• 95%

• 68%

In the first example, what is the mean of the history exam grades?

• 70

• 78

• 90

• 85

What is the standard deviation of the history exam grades in the first example?

• 5

• 6

• 7

• 8

To find the range that includes 95% of the grades, how many standard deviations should be considered?

• One

• Two

• Three

• Four

What is the lower bound of the range that includes 95% of the grades in the first example?

• 66

• 78

• 60

• 72

What is the upper bound of the range that includes 95% of the grades in the first example?

• 84

• 90

• 96

• 102

In the second example, what is the mean height of women?

• 170 cm

• 180 cm

• 160 cm

• 150 cm