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A scientist recorded the number of eggs in each of 10 birds'  [#permalink]

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Question Stats: 79% (00:45) correct 21% (00:55) wrong based on 1779 sessions

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A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?

(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.

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Difficulty: 650

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Re: A scientist recorded the number of eggs in each of 10 birds'  [#permalink]

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SOLUTION

A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?

The standard deviation of a set is always more than or equal to zero ($$SD\geq{0}$$). The standard deviation is 0 only when a set contains all identical elements (or which is same only 1 element).

(1) The average (arithmetic mean) number of eggs for the 10 nests was 4. Knowing the average does not help to get the standard deviation. Not sufficient.

(2) Each of the 10 nests contained the same number of eggs. So, the set contains all identical elements, which means that the standard deviation is zero. Sufficient.

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scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?

(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.

SD = Sqrt( sum(x-Mean)^2/n)

1 is INEFF as we can take two samples, sample one 5 nests were 3 and 5 nests were 5 - arithmetic means = 4.
another sample, 5 nests are 2 and 5 nests are 6, arithmetic mean 4 again but standard deviation (the dispersion of data points) is larger

2 is GOOD as the SD = 0, if all the same, no dispersion,

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Re: A scientist recorded the number of eggs in each of 10 birds'  [#permalink]

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Bunuel wrote:

A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?

(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.

St 1: Insufficient: Avg no of eggs for 10 nest is 4. ie total no of eggs are 40. So we can distribute it in 10 nests in various combinations. Hence the SD will vary accordingly.
St 2: Sufficient: Since each nest contains same no of eggs the SD is "0"

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The question can be simplified to " What is distribution of Eggs in 10 nests from the mean no of eggs"

Statement 1- Mean is given but no information is given regarding the distribution around mean.------> Insufficient.
Statement 2- As each nest contain the same no of eggs, there is '0' distribution around mean.------>Sufficient.

Hope it helps
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Statement 1: We know the mean but we don't have any other information to compute the SD. Insufficient.
Statement 2: If all the nests contain the same amount of eggs, the mean # of eggs would be the same as # eggs in every nest...no matter how many eggs there are the SD will always be 0. Sufficent.
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Bunuel wrote:
A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?

(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.

Practice Questions
Question: 38
Page: 278
Difficulty: 650

1. just mean provided no other data about eggs in each nest.. could be anything. No suff.

2. All nest has same # of egg . Hence SD=0 .. Suff
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GMAT 1: 760 Q50 V44 Re: A scientist recorded the number of eggs in each of 10 birds'  [#permalink]

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Bunuel wrote:
A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?

(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.

Standard Deviation is the distance of the elements of a set from the mean. Keeping this thing in mind helps solving most of the questions.
In majority of the questions, you will not be tested on your knowledge of the formula of SD

Required: standard deviation of the numbers of eggs in the 10 nests

Statement 1: The average (arithmetic mean) number of eggs for the 10 nests was 4
This does not tells us anything about the other elements. Hence we cannot find the SD
INSUFFICIENT

Statement 2: Each of the 10 nests contained the same number of eggs
This means that the average = no. of eggs in each nest.
Hence the SD = 0 (Distance from average = 0 if all the elements of a set are same)
SUFFICIENT

Option B
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Bunuel wrote:
A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?

(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.]

We are asked to determine the standard deviation of the number of eggs in 10 nests.

Statement One Alone:

The average (arithmetic mean) number of eggs for the 10 nests was 4.

Knowing only the average of the number of eggs for the 10 nests is not enough information to determine the standard deviation. Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Each of the 10 nests contained the same number of eggs.

Since we know that each nest had the same number of eggs, we know that the standard deviation must be zero.

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Re: A scientist recorded the number of eggs in each of 10 birds'  [#permalink]

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Bunuel wrote:
A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?

(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.

Target question: What was the standard deviation of the numbers of eggs in the 10 nests?

Statement 1: The average (arithmetic mean) number of eggs for the 10 nests was 4.
There are several scenarios that satisfy statement 1. Here are two:
Case a: the numbers are {4, 4, 4, 4, 4, 4, 4, 4, 4, 4, }, in which case the standard deviation is zero
Case b: the numbers are the numbers are {0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8}, in which case the standard deviation is NOT zero
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Each of the 10 nests contained the same number of eggs.
In other words, all 10 data values are the same, which means there is NO deviation among the values.
So, the standard deviation is zero
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Re: A scientist recorded the number of eggs in each of 10 birds'  [#permalink]

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1) mean is 4 , we dont know the number of eggs hence insufficient A,D gone
2) All contain equal number of eggs, lets say X X X X X X X X X X. mean is X and SD will be Zero = 0 therefore ans is B
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A scientist recorded the number of eggs in each of 10 birds'  [#permalink]

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Hi All,

To start, Standard Deviation is a relatively rare category on the GMAT (you'll likely see just one question that asks you about it) - and you'll never be asked to calculate S.D. using the S.D. Formula. As such, you'll really only be tested on the 'concept' of S.D. (and S.D. is basically a measure of how 'spread out' a group of numbers is).

We're told that a scientist recorded the number of eggs in each of 10 birds' nests. We're asked for the standard deviation of the numbers of eggs in the 10 nests.

1) The average (arithmetic mean) number of eggs for the 10 nests was 4.

With the average number of eggs, we know that there are a total of (10)(4) = 40 eggs, but we don't know the individual number in each nest (so we don't know how 'spread out' the numbers are).
Fact 1 is INSUFFICIENT

2) Each of the 10 nests contained the same number of eggs.

When all of the numbers in a sample are the SAME, that means that there is NO 'spread' and the S.D. is 0. With the information in Fact 2, we can answer the question.
Fact 2 is SUFFICIENT

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