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# The chart above represents the number of students at five schools, eac

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The chart above represents the number of students at five schools, eac [#permalink]
nguyendinhtuong wrote:
Bunuel wrote:

The chart above represents the number of students at five schools, each of which has branches in each of four towns. At which school is the standard deviation from the average number of students the least?

A. School 1
B. School 2
C. School 3
D. School 4
E. School 5

Attachment:
2017-01-25_1731.png

Solution 1.

School 1:
$$\overline{x_1} = \frac{148+151+153+148}{4}=\frac{600}{4}=150$$
$$\sigma^2_1=(148-150)^2 + (151-150)^2 + (153-150)^2 + (148-150)^2=2^2+1+3^2+2^2$$

School 2:
$$\overline{x_2} = \frac{156+99+148+157}{4}=\frac{560}{4}=140$$
$$\sigma^2_2=(156-140)^2 + (99-140)^2 + (148-140)^2 + (157-140)^2=16^2+41^2+8^2+17^2 > \sigma^2_1$$

School 3:
$$\overline{x_3} = \frac{104+120+196+140}{4}=\frac{560}{4}=140$$
$$\sigma^2_3=(104-140)^2 + (120-140)^2 + (196-140)^2 + (140-140)^2=36^2+20^2+56^2+0 > \sigma^2_1$$

School 4:
$$\overline{x_4} = \frac{95+156+204+35}{4}=\frac{490}{4}=122.5$$
$$\sigma^2_4=(95-122.5)^2 + (156-122.5)^2 + (204-122.5)^2 + (35-122.5)^2 > \sigma^2_1$$

School 5:
$$\overline{x_5} = \frac{217+74+159+220}{4}=\frac{670}{4}=167.5$$
$$\sigma^2_5=(217-167.5)^2 + (74-167.5)^2 + (159-167.5)^2 + (220-167.5)^2> \sigma^2_1$$

Hence the least standard deviation is from school 1. The answer is A.

Solution 2.

School 1. $$\{148;148;151;153\}$$
School 2. $$\{99;148;156;157\}$$
School 3. $$\{104;120;140;196\}$$
School 4. $$\{35;95;156;204\}$$
School 5. $$\{74;159;217;220\}$$

It's clear that the difference between any two elements in school 1 is the least. Hence, the standard deviation in school 1 will remain the least. The answer is A.

With due respect to quoted solution, I must tell all the readers that such calculations are strictly forbidden in a smart aptitude test like GMAT.

Solving question like this (using the formula of Standard deviation) is equivalent to killing time willingly.

Formula of standard deviation is NEVER to be used in GMAT
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The chart above represents the number of students at five schools, eac [#permalink]
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GMATinsight wrote:

With due respect to quoted solution, I must tell all the readers that such calculations are strictly forbidden in a smart aptitude test like GMAT.

Solving question like this (using the formula of Standard deviation) is equivalent to killing time willingly.

Formula of standard deviation is NEVER to be used in GMAT

I already knew that. I just wrote it to make the solution clearer. It's always clever to solve as quick as possible, but I think the test takers first need to understand what they are working with.
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Re: The chart above represents the number of students at five schools, eac [#permalink]
Bunuel wrote:

The chart above represents the number of students at five schools, each of which has branches in each of four towns. At which school is the standard deviation from the average number of students the least?

A. School 1
B. School 2
C. School 3
D. School 4
E. School 5

Attachment:
2017-01-25_1731.png

On arranging the sets in increasing order,we see that set A has the least deviation.