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Question:  If the mean of the set of number x1,x2...xn is ¯x ,then the mean of the number xi+2i,1n is 
Options:
A.¯x+2n
B.¯x+n+1
C.¯x+2
D.¯x+n
Answer: Option B
: B

¯x=ni=1xinni=1xi=n¯xni(xi+2i)n=ni=1xi+2(1+2+...+n)n=n¯x+2n(n+1)2n=¯x+(n+1)

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More Questions on This Topic :

Question 1. If the coefficient of variation of data pertaining to goals scored by two teams A and B in a football season are 2.5 and 7.2 respectively, then which of the following statements i strue?
  1.    Team B is more consistent than team A.
  2.    Two teams are equally consistent.
  3.    Team A is more consistent than team B.
  4.     The s.ds. of team A and team B are 125,172.
Answer: Option C
: C

We know that, lesser is the coefficient of variation, the data is more consistent.

Since C.V. of the team A is 2.5, which is less than the C.V. of team B, we can conclude that team A is more Consistent.
Question 2. The mean weight per student in a group of seven students is 55 kg if the individual weights of 6 students are 52, 58, 55, 53, 56 and 54; then weight of the seventh student is
  1.    55 kg
  2.    60 kg
  3.    57 kg
  4.    50 kg
Answer: Option C
: C

Total weight of 7 students is =55×7=385kg
Sum of weight of 6 students
=52+58+55+53+56+54=328kg
Weight of seventh student =385328=57kg.
Question 3. The mean deviation from the mean for the set of observations – 1, 0, 4 is
  1.    less than 3
  2.    less than 1 
  3.    greater than 2.5
  4.    greater than 4.9
Answer: Option A
: A

¯x=1+0+43=1.Mean Deviation =13[|11|+|01|+|41|]=2
Question 4. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations in the set is

 increased by 2, then the median of the new set
  1.    s increased by 2               
  2.    is decreased by 2
  3.    is two times the original median               
  4.    remains the same as that of the original set
Answer: Option D
: D

We know that median is found when we arrange the observations in ascending or descending order. And if the number of observations are odd then it is the n+12th term.
Since on arranging 9 observations 5th will be the median.
On changing 4 of any side won't affect the median and it'll remain same.

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