edited by
5,969 views
18 votes
18 votes

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
  1. $P$, $Q$
  2. $Q$, $R$
  3. $P$, $R$
  4. $R$, $S$
edited by

2 Answers

Best answer
28 votes
28 votes

Suppose we double each entry of a list

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

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

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

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


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

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

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

$\quad \quad \quad= 2  \sigma_I$

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. 

Correct Answer: $C$

edited by
Answer:

Related questions

33 votes
33 votes
2 answers
3
9 votes
9 votes
4 answers
4
gatecse asked Sep 29, 2014
2,667 views
Given the sequence of terms, $\text{AD CG FK JP}$, the next term is$\text{OV}$$\text{OW}$$\text{PV}$$\text{PW}$