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The arithmetic mean of 300 measurements is 72, and the arith
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24 Aug 2020, 10:19
24 Aug 2020, 10:19
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The arithmetic mean of 300 measurements is 72, and the arithmetic mean of 200 additional measurements is 64.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The arithmetic mean of the 500 measurements |
68 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: The arithmetic mean of 300 measurements is 72, and the arith
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24 Aug 2020, 10:19
24 Aug 2020, 10:19
Expert Reply
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
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Re: The arithmetic mean of 300 measurements is 72, and the arith
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24 Aug 2020, 13:52
24 Aug 2020, 13:52
1
Carcass wrote:
The arithmetic mean of 300 measurements is 72, and the arithmetic mean of 200 additional measurements is 64.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The arithmetic mean of the 500 measurements |
68 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
A combined average of two sets is the sum of all measurements over the total number of measurements.
The sum of \(300\) measurements of the data set with arithmetic mean \(72\) is \(300 \cdot 72 = 21600\).
The sum of \(200\) measurements of the data set with arithmetic mean \(64\) is \(200 \cdot 64 = 12800\).
Thus the sum of all measurements is \(21600 + 12800 = 34400\) and the total number of measurements is \(500\).
The arithmetic mean of the \(500\) measurements is \(\frac{34400 }{ 500} = 68.8\), which is greater than \(68\).
Hence, A is greater than B.
Therefore, A is the right answer.
