For any distribution regardless of shape the portion of data lying within k standard deviations (k > 1) of the mean is at least 1 – 1/(K^2)
Eg: mean = 6, Standard deviation = 3.84
For k = 2, at least 1 – 1/4 = 3/4 or 75% of the data lie within 2 standard deviation of the mean
For k = 3, at least 1 – 1/9 = 8/9 = 88.9% of the data lie within 3 standard deviation of the mean
Eg:
The mean time in a women’s 400-meter dash is 52.4 seconds with a standard deviation of 2.2 sec. Apply Chebychev’s theorem for k = 2
At least 75% of the women’s 400-meter dash times will fall between 48 and 56.8 seconds
