Question

1. Which of the following is true?

   1. Data sets with the same mean and the same standard deviation must have the same shape.
   2. The mean is less affected by extreme observations than the median.
   3. Chebyshev's Rule gives us an idea what proportion of the data set will fall within certain bounds, regardless of the shape of the distribution.

   		i. only
   		ii. only
   		iii. only
   		i. and iii.
   		None of the above.

Answer 1

Sol:

mean is affected by oitliers

median is not affected by outliers

Data sets with the same mean and the same standard deviation do not have the same shape

ex:

r and r1 have same mean and same sd

but different shape

rnorm1 <- function(n,mean,sd) { mean+sd*scale(rnorm(n)) }
r <- rnorm1(5,2,1)
mean(r) ## 4
sd(r)
r
rnorm2 <- function(n,mean,sd) { mean+sd*scale(rnorm(n)) }
r1 <- rnorm2(5,2,1)
mean(r1) ## 4
sd(r1)
r
r1

Chebyshev's Rule gives us an idea what proportion of the data set will fall within certain bounds, regardless of the shape of the distribution.

Is only true

iii. only