Question

Given a set of data that is skewed-left, there is at least _____ % of the data within 2 standard deviations.

Fill in the blank with the best answer:

0

68

75

89

95

99.7

Answer 1

Given a set of data that is skewed-left, there is at least 75 % of the data within 2 standard deviations.

Note: when data is not normal then we used Chebyshev's theorem for finding within standard deviation area.

According to Chebyshev's thereom, the proportion of values from a data set that will fall within k standard deviations of the mean will be at least (1 - 1 / k²), where k is a number greater than 1 (k is not necessarily an integer)

For k = 2

1 - (1/2²) = 0.75 = 0.75 * 100% = 75%