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A research report states that the average (arithmetic mean) of 120 mea

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A research report states that the average (arithmetic mean) of 120 mea  [#permalink]

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New post 10 Dec 2019, 01:09
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A research report states that the average (arithmetic mean) of 120 measurements was 72.5, the greatest of the 120 measurements was 92.8, and the range of the 120 measurements was 51.6.

The information given above is sufficient to determine the value of which of the following statistics?

I. The least of the 120 measurements
II. The median of the 120 measurements
III. The sum of the 120 measurements

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III


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A research report states that the average (arithmetic mean) of 120 mea  [#permalink]

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New post 10 Dec 2019, 03:21
Arithmetic mean=\(\frac{( a_1+a_2+...+a_n)}{120} = 72.5\)

—> \(a_n = 92.8\)
The range = \(a_n —a_1 = 51.6 \)

I. The least of the 120 measurements
—> \(a_1 = a_n —51.6 = 31.2\) (Yes)

II. The median of the 120 measurements— we don’t know whether the measurements are consecutive numbers. (No)

III. The sum of the 120 measurements
—> \(a_1+a_2+...+a_n= 120*72.5\) (yes)

We could find only I and III.
The answer is D

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Re: A research report states that the average (arithmetic mean) of 120 mea  [#permalink]

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New post 11 Dec 2019, 07:05
Bunuel wrote:
A research report states that the average (arithmetic mean) of 120 measurements was 72.5, the greatest of the 120 measurements was 92.8, and the range of the 120 measurements was 51.6.

The information given above is sufficient to determine the value of which of the following statistics?

I. The least of the 120 measurements
II. The median of the 120 measurements
III. The sum of the 120 measurements

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III


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n=120
avg=72.5
sum=n*avg
tn=92.8
rng=tn-a=51.6
a=92.8-51.6

Ans (D)
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Re: A research report states that the average (arithmetic mean) of 120 mea  [#permalink]

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New post 12 Dec 2019, 18:50
Bunuel wrote:
A research report states that the average (arithmetic mean) of 120 measurements was 72.5, the greatest of the 120 measurements was 92.8, and the range of the 120 measurements was 51.6.

The information given above is sufficient to determine the value of which of the following statistics?

I. The least of the 120 measurements
II. The median of the 120 measurements
III. The sum of the 120 measurements

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III


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Since we know the average and the quantity, we can determine the sum. Since we know the largest measurement and the range, we can determine the smallest measurement. However, it is not possible to determine the median of the 120 measurements from the information given to us.

Answer: D
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Re: A research report states that the average (arithmetic mean) of 120 mea   [#permalink] 12 Dec 2019, 18:50
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