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Each of the 4 students in a certain class read several books during th

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New post 28 Jan 2020, 01:45
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Each of the 4 students in a certain class read several books during the past month. What was the standard deviation of the numbers of books read by the 4 students during the past month?

(1) The range of the number of books read by the 4 students during the past month was 0.

(2) One of the 4 students read 5 books during the past month.

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Re: Each of the 4 students in a certain class read several books during th  [#permalink]

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New post 28 Jan 2020, 02:01
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Quote:
Each of the 4 students in a certain class read several books during the past month. What was the standard deviation of the numbers of books read by the 4 students during the past month?

(1) The range of the number of books read by the 4 students during the past month was 0.

(2) One of the 4 students read 5 books during the past month.


CONCEPT: Standard deviation depends on the following inputs
1) The number of terms in the set. (Which is given in this question as 4)
2) The gaps between the terms when arranged in increasing order


Question: FInd the standard deviation of number of books read by the 4 students?

Statement 1: The range of the number of books read by the 4 students during the past month was 0

Range = Highest - Lowest = 0 (Given)
i.e Highest = Lowest
i.e. Highest number of books read by any student = Lowest number of books read by any student

Since the gaps between the terms is ZERO, therefore Standard Deviation of the set = 0
SUFFICIENT

Statement 2:One of the 4 students read 5 books during the past month.

The statemebnt doesn't give any information about the gaps between the terms. The value of one term in set can NOT lead us to any conclusion about the standard deviation of teh set hence

NOT SUFFICIENT

Answer: Option A
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Re: Each of the 4 students in a certain class read several books during th  [#permalink]

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New post 28 Jan 2020, 02:24
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Answer is A

Stmt1- If the range of a set that represents no of books read is 0, then it means that it is a set of positive integers with a range 0. So no one has read any books so SD is 0. This is sufficient

Stmt2: only one value in the set is given. There is no indication of how many books other 3 students read. This is insufficient for SD

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Re: Each of the 4 students in a certain class read several books during th  [#permalink]

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New post 28 Jan 2020, 02:57
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Quote:
Each of the 4 students in a certain class read several books during the past month. What was the standard deviation of the numbers of books read by the 4 students during the past month?

(1) The range of the number of books read by the 4 students during the past month was 0.

(2) One of the 4 students read 5 books during the past month.


sd is the measure of the dispersion of the dataset relative to its mean; if all datapoints are the same, the sd=0, if not, then the sd>0; the greater the difference between datapoint and the mean the greater the sd, and the closer the datapoint is to the mean, the smaller the sd.

(1) The range of the number of books read by the 4 students during the past month was 0. sufic

range=0 then, all datapoints are equal, thus sd=0.

(2) One of the 4 students read 5 books during the past month. insufic

s1: 5, but the others are unknown.

Ans (A)
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Re: Each of the 4 students in a certain class read several books during th  [#permalink]

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New post 28 Jan 2020, 04:38
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(1) The range of the number of books read by the 4 students during the past month was 0. That means there would be no deviation (or standard deviation =0).
SUFFICIENT

(2) One of the 4 students read 5 books during the past month.
We don't know how many books read by each of the other three students.
NOT SUFFICIENT.

FINAL ANSWER IS (A)

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Re: Each of the 4 students in a certain class read several books during th  [#permalink]

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New post 28 Jan 2020, 06:15
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1.The range is the highest number minus the lowest; if the range is 0 therefore all the numbers are the same meaning the sd is also 0
Sufficient
2. We don’t know the other numbers
Insufficient

Therefore
A

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Re: Each of the 4 students in a certain class read several books during th  [#permalink]

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New post 28 Jan 2020, 07:03
#1
The range of the number of books read by the 4 students during the past month was 0.
means all value are equal or say identical so the SD would be 0 as well ; sufficient
#2
One of the 4 students read 5 books during the past month.
other students books info not know ; insufficient
IMO A



Each of the 4 students in a certain class read several books during the past month. What was the standard deviation of the numbers of books read by the 4 students during the past month?

(1) The range of the number of books read by the 4 students during the past month was 0.

(2) One of the 4 students read 5 books during the past month.
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Re: Each of the 4 students in a certain class read several books during th  [#permalink]

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New post 28 Jan 2020, 07:57
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Four students read some books within the previous month. We are to determine the SD of the books read by the four students.

Statement 1: The range of the number of books read by the 4 students during the past month was 0.
From statement 1 above, we can conclude that the four students read the same number of books in the previous month since the range is 0. And once the range is zero, it means that the standard deviation is 0 as well. Statement 1 is sufficient.

Statement 2: One of the 4 students read 5 books during the past month.

Clearly insufficient. The remaining three students could each read 5 books as well in which case the SD is zero. They could each read 6 books or any number of books different from 5 in which case SD is not zero.

The answer is A.

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Re: Each of the 4 students in a certain class read several books during th  [#permalink]

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New post 28 Jan 2020, 11:33
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1) Sufficient :If the range is zero, then all of the numbers are the same and the standard deviation is zero.

2) Insufficient

A
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Re: Each of the 4 students in a certain class read several books during th   [#permalink] 28 Jan 2020, 11:33
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