BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:13 am

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.

Answer: B
Source: official guide

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