Also known as The 68-95-99.7 Rule Original content by D.R.S. The Empirical Rule Also known as The 68-95-99.7 Rule Original content by D.R.S.

What The Empircal Rule Says If the data is distributed in a bell-shaped distribution, then Approximately 68% of the data falls within one standard deviation, plus or minus, from the mean Approximately 95% of the data falls within two standard deviations of the mean Approximately 99.7% of the data falls within three standard deviations of the mean

What’s different from Chebyshev Chebyshev’s Rule The Empirical Rule Applies to any old distribution, any data set, no restrictions It makes timid claims because we have no guarantees about the data distribution pattern. It talks in terms of “ at least ____% of the data,” could be more, could be lots more Applies only to data sets which have a bell-shaped distribution pattern It makes stronger claims, because we know about the bell shape It talks in firm values, a definite approximate % of the data.

The Empirical Rule says… 68% of the data lives within one standard deviation of the mean, between z = _____ and z = _____

The Empirical Rule says… 95% of the data lives within two standard deviations of the mean, between z = _____ and z = _____

The Empirical Rule says… 99.7% of the data lives within three standard deviations of the mean, between z = _____ and z = _____

Outside of the middle 68% of the data lives within 1 stdev of mean So _____% lives outside, >1 stdev of the mean _____% in the left tail, _____% in the right tail

Outside of the middle 95% of the data lives within 2 stdevs of mean So _____% lives outside,>2 stdevs of the mean _____% in the left tail, _____% in the right tail

Outside of the middle 99.7% of the data within 3 stdevs of mean So _____% lives outside,>3 stdevs of the mean _____% in the left tail, _____% in the right tail

Practice with Areas: 0 < z < 1 _____% of the data lies between z = -1 and z = +1 And this area is ½ of that, or _____%

Practice with Areas: 0 < z < 2 _____% of the data lies between z = -2 and z = +2 And this area is ½ of that, or _____%

Practice with Areas: 0 < z < 3 _____% of the data lies between z = -3 and z = +3 And this area is ½ of that, or _____%

Practice with Areas: 0 < z <∞ Since the bell-shaped curve is SYMMETRIC, _____ % lies to the right of z = 0.

Practice with Areas: -∞ < z < 0 Since the bell-shaped curve is SYMMETRIC, _____ % lies to the right of z = 0.

Practice with Areas: -∞ < z < -1 _____ % of the area lies to the left of z = 0 But we take away the area between z = -1 to 0 ½ of the area between z = -1 and z = +1, ½ of ___% Summary: _____ % minus _____ % = _____%

Practice with Areas: -∞ < z < -2 _____ % of the area lies to the left of z = 0 But we take away the area between z = -2 to 0 ½ of the area between z = -2 and z = +2, ½ of ___% Summary: _____ % minus _____ % = _____%

Practice with Areas: -∞ < z < 1 ____ % to the left of z = 0, Plus the area between z = 0 and z = 1 Total area between z = -1 and z = +1 is ______% Half of that is ____% Summary: ____% + ____% = _____%

Practice with Areas: -∞ < z < 2 ____ % to the left of z = 0, Plus the area between z = 0 and z = 2 Total area between z = -2 and z = +2 is ______% Half of that is ____% Summary: ____% + ____% = _____%

Practice with Areas: -∞ < z < 3 ____ % to the left of z = 0, Plus the area between z = 0 and z = 3 Total area between z = -3 and z = +3 is ______% Half of that is ____% Summary: ____% + ____% = _____%

Practice with Areas: -∞ < z < ∞ Should be a cinch, right? ____ %

Practice with Areas: 1 < z < 2 Area between z = 0 and z = 2 is ½ of ____% which is ____% Area between z = 0 and z = 1 is ½ of ____% which is ____% Subtract: ____% - ____% = ____%

Practice with Areas: 1 < z < 3 Area between z = 0 and z = 3 is ½ of ____% which is ____% Area between z = 0 and z = 1 is ½ of ____% which is ____% Subtract: ____% - ____% = ____%

Practice with Areas: 1 < z < ∞ ____ % in the right half, 0 to ∞ Minus the ____% between 0 and 1 Equals _____%

Practice with Areas: 2 < z < 3 Area between z = 0 and z = 3 = _____% Area between z = 0 and z = 2 = _____ % Subtract, giving ____% between 2 and 3

Practice with Areas: 2 < z < ∞ ____% in the right half Minus _____% between 0 and 2 Equals ____% to the right of z = 2.

Practice with Areas: -3 < z < 0 _____% between z = -3 and z = +3 Half of that is _____%

Practice with Areas: -2 < z < 0 _____% between z = -2 and z = +2 Half of that is _____%

Practice with Areas: -1 < z < 0 _____% between z = -1 and z = +1 Half of that is _____%

Practice with Areas: -3 < z < 1 ____ % between z = -3 and z = 0 ____ % between z = 0 and z = 1 Add, giving _____%

Practice with Areas: -3 < z < 2 ____ % between z = -3 and z = 0 ____ % between z = 0 and z = 2 Add, giving _____%

Practice with Areas: -2 < z < -1 ____% between z = -2 and z = 0 ____% between z = -1 and z = 0 Subtract, giving ____%

Practice with Areas: -2 < z < 1 ____ % between z = -2 and z = 0 ____ % between z = 0 and z = 1 Add, giving _____%

Practice with Areas: -2 < z < 3 ____ % between z = -2 and z = 0 ____ % between z = 0 and z = 3 Add, giving _____%

Practice with Areas: -1 < z < 3 ____ % between z = -1 and z = 0 ____ % between z = 0 and z = 3 Add, giving _____%

Practice with Areas: -1 < z < 2 ____ % between z = -1 and z = 0 ____ % between z = 0 and z = 2 Add, giving _____%