Question

Use Chebyshev’s theorem to find what percent of the values will fall between 162 and 292 for a data set with a mean of 227 and standard deviation of 13.

Answer 1

i really don't understand the way the book explains this

Answer 2

In elementary stats we just brushed over Cheby. But

Use Chebyshev’s theorem to find what percent of the values will fall between 161 and 229 for a data set with mean of 195 and standard deviation of 17.

a) The interval (161, 229) can be written as (195-2*17, 195+2*17) which is same as (Mean -k*SD, Mean +k*SD), where k =2.

According to Chebyshev’s theorem, at least 1 - (1/k-squared) of the measurements will fall within (Mean -k*SD, Mean +k*SD)

But 1 - (1/k-squared) = 1 - (1/2^2) = 1 – 0.25= 0.75

Thus 75 percent of the values will fall between 161 and 229 for a data set with mean of 195 and standard deviation of 17.

Answer 3

This problem seems to match yours quite nicely :)

Answer 4

each of your values falls at 5 sd from the mean:

227
-162
------
65 ; /13 = 5

Cheb thrm says: 1-(1/5^2) will work to cover the span from -5sd to 5sd

1 - 1/25 = 24/25 = .96, or 96%