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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A research report states that the average (arithmetic mean) of 120 mea

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

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Difficulty:   15% (low)

Question Stats: 87% (01:02) correct 13% (01:23) wrong based on 39 sessions

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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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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.

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

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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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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

Are You Up For the Challenge: 700 Level Questions

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.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: A research report states that the average (arithmetic mean) of 120 mea   [#permalink] 12 Dec 2019, 18:50
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# A research report states that the average (arithmetic mean) of 120 mea  