BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

PREP TEST 2

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Sun Jul 27, 2008 8:59 am
Thanked: 1 times

PREP TEST 2

by Oxana » Mon Sep 01, 2008 4:58 pm
a certain list of 100 data has an average of 6 and standard deviation d, where d is a positive. Which of the following pairs of data when added to the list must result in a list of 102 data with standard deviation less than d?

-6 and 0
0 and 0
0 and 6
0 and 12
6 and 6


ans E
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 135
Joined: Mon Jun 23, 2008 3:56 am
Thanked: 7 times

by sethids » Mon Sep 01, 2008 5:07 pm
The standard deviation of a list would come down if the data points are closer to the mean.

The mean of the given list is 6 so the data pair 6 and 6 is closest (amongst the given options) to the mean and thus reduces the SD of the entire list (when added to the list)less than the current SD.
Top
Legendary Member
Posts: 594
Joined: Thu Aug 14, 2008 11:51 pm
Thanked: 12 times

by nervesofsteel » Tue Sep 02, 2008 12:01 am
sd = sqrt { [(x-x1)^2 + (x-x2)^2 + .... ]/N}

X - mean
x1 is the frist number , x2 is the second.. etc
N = total numbers

Now our aim is to decrease the SD when 2 new number are added...
N will be increased from 100 to 102

x =6..

So not to increase the sum in numerator.. we can add to numbers as 6,6..
as x-6 = 6-6 =0 in both cases but denominator has increased.. thus the overall SD has decreased....
Top
Post new topic Post Reply
• Page 1 of 1