Problem Solving

A set of data consists of the following 5 numbers: 0,2,4,6 and 8.Which two numbers,if added to create a set of 7 numbers will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
A.-1 and 9
B. 4 and 4
C. 3 and 5
D. 2 and 6
E. 0 and 8


OA is D

A lot of calculations is necessary to solve this problem...Is there any shortcut method to solve this problem?

I'm not sure that this is the answer. However, can't you assume that since SD measures the variation between the numbers in the set and the mean ( which is 4), that the SD is 2. Therefore, adding 2 and 6 will keep the sd the same? Right?

raju232007 wrote:A set of data consists of the following 5 numbers: 0,2,4,6 and 8.Which two numbers,if added to create a set of 7 numbers will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
A.-1 and 9
B. 4 and 4
C. 3 and 5
D. 2 and 6
E. 0 and 8


OA is D

A lot of calculations is necessary to solve this problem...Is there any shortcut method to solve this problem?

I go with D as well...

Though Not sure if a shorter method available but this one sure works..

0 2 4 6 8 mean 4
variance= ( X-m)^2 /N which is 2*(2^2+ 4^2)/5 = 8

now need 2 number to be added to maintain the variance

assume them as X and Y are variances ....

we know that

40 + X+Y/7 = 8

X+Y = 16

(X-4)^2 + (Y-4)^2 = 16

only D gives u the closest choice...

if u know the formula well.. all it takes is 1 minutes...

Hope that helps..

if i am right the formula for std deviation is sqrt(sum of (X-m)^2/N)...and so the standard deviation for the given 5 nos is sqrt(40^2/5)which is sqrt(320)...


Now we are supposed to find out which of the two numbers if included along with the 5 nos will work out to the closest std deviation i.e sqrt(320)

I calculated the ans using the longest method possible...and that is as follows

if we consider the first choice -1 and 9

Given set : 0 2 4 6 8
New set(X) : -1 0 2 4 6 8 9
Mean(m) : 4
X-m : -5 -4 -2 0 2 4 5
(X-m)^2 : 25 16 4 0 4 16 25
sum of (X-m)^2 :90
std deviation=sqrt(90^2)/5 = sqrt(1620)

In the same manner i calculated the std deviation for the other choices which took a lot of time and i found that choice D has a std deviation i.e sqrt(336) which is close to the desired value...i.e sqrt(320)

raju232007 wrote:if i am right the formula for std deviation is sqrt(sum of (X-m)^2/N)...and so the standard deviation for the given 5 nos is sqrt(40^2/5)which is sqrt(320)...


Now we are supposed to find out which of the two numbers if included along with the 5 nos will work out to the closest std deviation i.e sqrt(320)

I calculated the ans using the longest method possible...and that is as follows

if we consider the first choice -1 and 9

Given set : 0 2 4 6 8
New set(X) : -1 0 2 4 6 8 9
Mean(m) : 4
X-m : -5 -4 -2 0 2 4 5
(X-m)^2 : 25 16 4 0 4 16 25
sum of (X-m)^2 :90
std deviation=sqrt(90^2)/5 = sqrt(1620)

In the same manner i calculated the std deviation for the other choices which took a lot of time and i found that choice D has a std deviation i.e sqrt(336) which is close to the desired value...i.e sqrt(320)

Ur calculation of SD is wrong ..
ur right on the formula ..but execution is wrong ...

u know that the mean is 4
thus SD is

sq rt [(X-m)^2/N]
X is each number for instance for 0 2 4 6 8 X will take each of those numbers

thus its

sqrt[ (0-4)^2 + (2-4)^2 + ( 4 -4)^2 + (6-4)^2 + (8-4)^2 ] /5

16 +4+ 4 + 16 = 40/5 =8

thus its sqrt 8 = 2.8

hope that helps ..

Thanks for the clarification.... 8)

I still have a doubt on the OA

as i went on to solve my answers for the options provided are
sqrt(13)
sqrt(8)....this is eight
sqrt(6)
sqrt(7)(appro)
sqrt(10)(appro)

thus having 4 and 4 added to number stream does not make any change to the sd hence i would go for B ofcourse the next best choice is D

Regards

I am sorry i made the basic claculation error for b divided the resultant with 5...infact i fell into trap of calculating i should have right away eliminated B

my earlier next best choice ofcourse is the answer

oh i was just wondering whether the OA is ever wrong!!!! this one is real

Not sure how 2 and 6 satisfies the equation:

(X-4)^2 + (Y-4)^2 = 16 .

I thought 0 and 8 should satisfy? Can you please clarify?