Set problem

[yalanand]

S = {-20, -15, -5, 10, 10, 15, 40}. Which of the following are true?

I. The median of S is greater than the mean of S.
II. The standard deviation of S is greater than the range of S.
III. The range of S is twice the mode of S.

(A) I
(B) I and II
(C) I and III
(D) II and III
(E) III

[piyush_nitt]

S = {-20, -15, -5, 10, 10, 15, 40}. Which of the following are true?

I. The median of S is greater than the mean of S.
II. The standard deviation of S is greater than the range of S.
III. The range of S is twice the mode of S.

(A) I
(B) I and II
(C) I and III
(D) II and III
(E) III

Median = 10
mean = 5
range = 40-(-20) = 60
mode = 10

1. median > mean - true
2. As mean = 5
range = 60
sd will be less than range. - false
3.false

IMO A

[yalanand]

Well done...correct

[DeepakR]

Can someone explain the Standard deviation step alone in #2 ?

[sanjay_dce]

Can someone explain the Standard deviation step alone in #2 ?

S,D =(summ (xi-mean X)^2) ^1/2

I hope this helps it is also called root mean square of the deviations.

say if given values of x are 1,2,3,4,5

so obviously mean x = 3 ( i hope u already know this)
then x1-mean x = 1-3 = -2 , now square of -2 = 4
similarly x2-mean x = 2-3 = -1 now square of -1 = 1
and x3-meanx= 0 = 0

and all values are 1 and 4

now sum all these values = 1=4+0+1+4 = 10 and take square root of 10, ,, hence square root(10) is the std deviation of the given data set

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