The numbers in set P denote the distance of certain positive integers

Question

The numbers in set P denote the distance of certain positive integers from -1 on the number line. The numbers in set Q denote the distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?

A. Standard Deviation (P) = Standard Deviation (Q)
B. Standard Deviation (P) = - Standard Deviation (Q)
C. Standard Deviation (P) = Standard Deviation (Q) + 2
D. Standard Deviation (P) = 2* Standard Deviation (Q)
E. None of the above

stne · Answer

Let us choose appropriate integers.

Let the original set be  { 6,8,11,15,20 }

P  = {7,9,12,16,21}

Q  = {5,7,10,14,19}

Mean of P  = 13 
Mean of Q  = 11

Deviation from Mean for P  ={ 6,4,1,3,8} 
Devaition from Mean for Q  = { 6,4,1,3,8}

Since both P and Q have the same deviation from the mean, they will have the same SD.

Ans A

Note: A smaller appropriate mother set could also be chosen to see the relation between P and Q

Hope it helps.

gmatophobia · Answer

Key information to notice in this question is the fact that all the distances are of "positive integers" which means that all the numbers lie on the same side of -1. Let's assume that there are n numbers and the distances of those numbers from -1 are d_1 , d_2, d_3 , .... d_n So set P = { d_1, \quad d_2, \quad d_3, \quad .... \quad,\quad d_n } SD of P = x Now the distances of those numbers from 1 will be d_1-2 , d_2-2, d_3-2 , .... d_n-2 We can visualize this over a number line ----------- -1 ----------------- 0 ----------------- 1 ----------------------- n ---------------- ----------- -1 <----------------------------- d ----------------------------> n --------------- ----------- -1 -------------------------------------- 1 <-------(d-2)------> n --------------- Therefore Q = { d_1-2, \quad d_2-2, \quad d_3-2, \quad .... \quad,\quad d_n-2 } If the same constant is added or subtracted from every term in the set, the SD of the set doesn't change. Hence SD(P) = SD(Q) Option A

shubhim20 · Answer

Bunuel   KarishmaB  HOW TO SOLVE THIS & HOW TO CHOOSE NUMBER FROM THE SET

stne · Answer

I think you are asking how to choose the mother set?

Mother set can be any set.

Let M be  1,2,3

P  = 2,3,4  : Distance of each member of mother set from  -1

Q  = 0,1,2  : Distance of each member of mother set from  1

Mean of P  = 3 
Mean of Q  =1

Deviation of Set P from its mean  = {1,0, 1} 
Deviation of set Q from its mean  = {1,0,1}

Since both sets have the same deviation from their respective means, hence both will have the same SD.

Hope it's clear now?

KarishmaB · Answer

Given a set of positive integers (they can take values 1, 2, 3, 4, 5, etc. only), if the distance of a number from -1 is d, its distance from 1 will be (d-2). Think about it on the number line. Say the number 5. It is 6 units away from -1 and only 4 units away from 1. So 6 will be in set P and 4 will be in set Q.
This means that the numbers in Q will be (each number in set P - 2).
If you subtract 2 from each number of a set, its mean decreases by 2 but its SD remains unchanged. 
That is why the SD of P and Q will be the same.

Answer (A)

The numbers in set P denote the distance of certain positive integers

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The numbers in set P denote the distance of certain positive integers

Prep Toolkit

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