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A scientist recorded the number of eggs in each of 10 birds'

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by jjjinapinch » Thu Aug 03, 2017 11:54 am

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Answers

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B

C

D

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Difficulty—

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.

Official Guide question
Answer: B
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Aug 03, 2017 12:28 pm
jjjinapinch 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.

Official Guide question
Answer: B
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

Answer: B

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by [email protected] » Fri Aug 04, 2017 11:30 am
Hi jjjinapinch,

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

Final Answer: B

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by Scott@TargetTestPrep » Fri Aug 03, 2018 2:10 pm
jjjinapinch 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.

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.

Answer: B

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