Question

2. Are the following statements true or false and explain why?
(a) The median must always be a value in your data set. F but why
(b) If given PXi and n, we can find the standard deviation of X. F but why
(c) The standard deviation of X must always be positive F but why

Answer 1

a) Median is the middle value of data set

FALSE

Reason-- !,2,3,4

Median of the data set = (2+3)/2= 2.5 which is not the part of given data set.

$b) \ Standard \ deviation= \sqrt{E[x^2]-(E[x])^2}$

  $= \sqrt{\sum x^2p(x)-(\sum xp(x))^2}$

  $or, SD=\sqrt{ \frac{ \sum (x-\overline{x})^2}{n-1}}$

Mean is required which can not be find with Pxi and n only

c) Standard deviation can be Zero too.

so, Standard deviation is non-negative

Example = 2,2,2,2,2,2

standard dev = 0