Question

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

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

• It is to be noted that If all the values in a data set are equal to the same number, say $x$, then the average of the data set is $x$, the difference between each data value and the average is $x–x=0$, the sum of the squares of these differences is $0$, and so the standard deviation is $0$. On the other hand, if the values in a data set are not all equal to the same number, then the standard deviation will be positive.
  

1. If each of the $10$ nests had $4$ eggs, then the average would be $4$ and the standard deviation would be $0$. If $8$ nests had $4$ eggs, $1$ nest had $3$ eggs, and $1$ nest had $5$ eggs, then the average would be $4$ and the standard deviation would be positive; NOT sufficient.
2. Since all of the data values are equal to the same number, the standard deviation is $0$; SUFFICIENT. The correct answer is B; statement 2 alone is sufficient.