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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?

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.

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

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11 Sep 2012, 08:13

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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,

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

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12 Sep 2012, 04:02

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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"

Hence Answer is B
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12 Sep 2012, 13:20

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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.

Answer B

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

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24 Jan 2013, 13:19

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.

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

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.

The answer is B.
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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.

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

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

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17 Aug 2017, 02:21

Answer is B

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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