Question

A. Using 2^k  rule determine the number of classes you are recommended to use when construction a frequency distribution for the sample of data with 47 observation.

B. Using chebyshev's theorem calculate the minimum proportion of data contained with 1.5 standard deviations of its mean regardless of how the data is distributed. report your answer as decimal (not a percentage) measured to 3 decimal places for example, if you think the answer is 64.2% type 0.642 in the space for your response below

Answer 1

A)

Number of observations, n = 47

The numbef of classes k will the least k for which

Thus, k = 6 is the least integral k which satisfies the above inequality

The required number of classes = 6

B)

Using Chebyshev's Theorem, the minimum proportion of data within k standard deviations of the mean is

Thus, the minimum proportion of data contained within 1.5 standard deviations of its mean = = 5/9

= 0.556