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SD

by shashank.ism » Tue Feb 16, 2010 4:01 am
What is the standard deviation (SD) of the four numbers p, q, r, s?
1. The sum of p, q, r and s is 24
2. The sum of the squares of p, q, r and s is 224
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Source: — Data Sufficiency |
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by ajith » Tue Feb 16, 2010 4:40 am
shashank.ism wrote:What is the standard deviation (SD) of the four numbers p, q, r, s?
1. The sum of p, q, r and s is 24
2. The sum of the squares of p, q, r and s is 224
SD =sqrt( (avg - p)^2+ (avg-q)^2 + (avg-r)^2 + (avg-s)^2)/3)
= sqrt( (4*avg^2 - 2*avg(p+q+r+s) + p^2+q^2+r^2+s^2)/3)


1. is not sufficient since it only allows us to calculate average
2. is not sufficient since it only allows us to calculate p^2+q^2+r^2+s^2

Combined is sufficient
Hence C

[ I do not think this concept is tested in GMAT so , if anybody is finding difficulty following this please avoid this question]
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by sanju09 » Tue Feb 16, 2010 6:02 am
ajith wrote:
shashank.ism wrote:What is the standard deviation (SD) of the four numbers p, q, r, s?
1. The sum of p, q, r and s is 24
2. The sum of the squares of p, q, r and s is 224
SD =sqrt( (avg - p)^2+ (avg-q)^2 + (avg-r)^2 + (avg-s)^2)/3)
= sqrt( (4*avg^2 - 2*avg(p+q+r+s) + p^2+q^2+r^2+s^2)/3)


1. is not sufficient since it only allows us to calculate average
2. is not sufficient since it only allows us to calculate p^2+q^2+r^2+s^2

Combined is sufficient
Hence C

[ I do not think this concept is tested in GMAT so , if anybody is finding difficulty following this please avoid this question]
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by kstv » Tue Feb 16, 2010 9:58 am
Concept of SD is tested in GMAT. See 12th OG Maths Review Arithmetic. Just the concept that SD = √Σ(x- Mean)^2/No of elements.

Mean is given = 24/4 = 6

p^2 + q^2 ..... is given

So SD = √ (p^2- Mean)^2 + (q^2- 6 )^2 ......

p^2 + q^2 ..... -2X Mean (p+q+..) + 4 (Mean )^2

√(224 - 12 (24) + 4 X 36)/ 4

So C
Last edited by kstv on Tue Feb 16, 2010 10:10 am, edited 1 time in total.
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by sumanr84 » Tue Feb 16, 2010 10:10 am
Standard deviation is not as commonly tested, but if you're scoring at a high level on the Quantitative Section on test day, you may well see a question on this topic.

For NewBies,

https://www.beatthegmat.com/mba/2009/08/ ... -deviation
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