Question

5. Applying Chebyshev’s Theorem: (Be as detailed as possible thanks)

a. According to the Chebyshev’s theorem, at least what percentage of the data fall within 2 standard deviations either side of the mean?

b. What’s the actual percentage of the data fall within 2 standard deviations either side of the mean?

c. According to the Chebyshev’s theorem, at least what percentage of the data fall within 3 standard deviations either side of the mean?

d. What’s the actual percentage of the data fall within 3 standard deviations either side of the mean?

Ans from my teacher. 75%, 34/37=92%, 8/9, 100%

Answer 1

a)from Chebychev ; % of values k standard deviation from mean =(1-1/k²)*100

hence percentage of the data fall within 2 standard deviations either side of the mean

=(1-1/2²)*100=(3/4)*100 =75.0%

b)for this the data is required which is not available here ;it seems 34 of 37 data values are within 2 standard deviation from the answer

c)

percentage of the data fall within 3 standard deviations either side of the mean =(1-1/3²)*100

=(8/9)*100=88.89%

d)

data is required which is not available here ;it seems 37 of 37 data values are within 3 standard deviation