For 6 days of work, a carpenter had daily earnings of $110, $120, $110

Question

For 6 days of work, a carpenter had daily earnings of $110, $120, $110, $100, $100, and $120, respectively. In which of the following intervals does the standard deviation of the daily earnings lie?

A. Between $110 and $120
B. Between $100 and $110
C. Between $50 and $60
D. Between $10 and $20
E. Between $0 and $10

gchandana · Answer

Official Explanation

Bunuel · Answer

For 6 days of work, a carpenter had daily earnings of $110, $120, $110, $100, $100, and $120, respectively. In which of the following intervals does the standard deviation of the daily earnings lie?

A. Between $110 and $120
B. Between $100 and $110
C. Between $50 and $60
D. Between $10 and $20
E. Between $0 and $10

We have the following list in ascending order:

{100, 100,  110 ,  110 , 120, 120}

The mean daily earning is 110.

The absolute differences from the mean are:

{10, 10, 0, 0, 10, 10}

Since every earning is within 10 of the mean, the standard deviation cannot exceed 10. Since two of the differences are 0, the standard deviation is actually less than 10.

Therefore, the standard deviation lies between $0 and $10.

Answer: E.

Bunuel · Answer

Similar questions to practice: https://gmatclub.com/forum/the-prices-f ... 58339.html https://gmatclub.com/forum/the-weights- ... 58430.html

MartyMurray · Answer

For 6 days of work, a carpenter had daily earnings of $110, $120, $110, $100, $100, and $120, respectively. In which of the following intervals does the standard deviation of the daily earnings lie?

The standard deviation of a group of values is basically, though not exactly, the average of the absolute differences between the values and the mean of the values. For the purpose answering of GMAT Standard Deviation questions, that basic understanding of standard deviation is sufficient.

So, to approximate the standard deviation of the 6 values, we can do the following.

Find the mean:

In this case, we don't have to do much math to find the mean because the values are centered around 110.

110, 100, 110, 110, 120, 120

Since the mean of 120 and 100 is 110, the mean of all the values must be 110 .

Approximate the standard deviation:

The absolute difference between 100 and the mean, 110, is 10.

The absolute difference between 120 and the mean, 110, is 10.

The absolute difference between 110 and the mean, 110, is 0.

So, the average absolute difference between the values and the mean is between 0 and 10.

A. Between $110 and $120
B. Between $100 and $110
C. Between $50 and $60
D. Between $10 and $20
E. Between $0 and $10

Correct answer:   E

For 6 days of work, a carpenter had daily earnings of $110, $120, $110

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GMAT Problem Solving (PS) Questions

For 6 days of work, a carpenter had daily earnings of $110, $120, $110

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