GATE CSE
First time here? Checkout the FAQ!
x
+3 votes
402 views

Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list 

Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list 

R: Doubling each entry in a list doubles the mean of the list

S: Doubling each entry in a list leaves the standard deviation of the list unchanged


(A) P, Q
(B) Q, R
(C) P, R
(D) R, S

asked in Numerical Ability by Veteran (12.9k points)   | 402 views

2 Answers

+13 votes
Best answer

Suppose we double each entry of a list


Initial Mean $(M_I)=\frac{ \sum_{i=1}^{n} x_i}{n}$

New Mean $(M_N)= \frac{\sum_{i=1}^{n}2\times x_i}{n}$

$=\frac{2}{n} \sum_{i=1}^{n}x_i$

So, when each entry in the list is doubled, mean also gets doubled.




Standard Deviation $\sigma_I = \sqrt {\sum_{i=1}^{n} \left(M_I - x_i\right)^2}$

New Standard Deviation $\sigma_N = \sqrt {\sum_{i=1}^{n} \left(M_N - 2 \times x_i\right)^2}$

$= \sqrt {\sum_{i=1}^{n} \left(2 \times \left(M_I - x_i\right)\right)^2}$

$= 2  \sigma_I$

So, when each entry is doubled, standard deviation also gets doubled. 


 

When we add a constant to each element of the list, it gets added to the mean as well. This can be seen from the formula of mean. 
 

 


When we add a constant to each element of the list, the standard deviation (or variance) remains unchanged. This is because, the mean also gets added by the same constant and hence the deviation from the mean remains the same for each element.



So, here P and R are correct. 

answered by Veteran (285k points)  
edited by
Mean = (x1+x2+x3+...+xn)/n
The answer has "the division by n" part missing.
Thanks :) Corrected now..
+1 vote
C. P,R are correct.
answered by Loyal (3.4k points)  


Top Users May 2017
  1. akash.dinkar12

    3338 Points

  2. pawan kumarln

    2108 Points

  3. Bikram

    1922 Points

  4. sh!va

    1682 Points

  5. Arjun

    1614 Points

  6. Devshree Dubey

    1272 Points

  7. Debashish Deka

    1208 Points

  8. Angkit

    1056 Points

  9. LeenSharma

    1018 Points

  10. Arnab Bhadra

    812 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 May 22 - 28
  1. Bikram

    1008 Points

  2. pawan kumarln

    734 Points

  3. Arnab Bhadra

    726 Points

  4. Arjun

    342 Points

  5. bharti

    328 Points


22,893 questions
29,196 answers
65,302 comments
27,695 users