Arrange the following sets in the order of the increasing magnitude of

Question

Arrange the following sets in the order of the increasing magnitude of their mean to standard deviation ratio.

I. {50, 60, 70, 80}
II. {35, 40, 45, 50}
III. {90, 110, 130, 150}

A. I < II < III
B. II < III < I
C. II < I < III
D. III < I < II
E. III < II < I

sanjitscorps18 · Answer

I. {50, 60, 70, 80}
Mean = 65
Mean to SD ratio ≈ 2.9

II. {35, 40, 45, 50}
Mean = 42.5
Mean to SD ≈ 4.7

III. {90, 110, 130, 150}
Mean = 120
Mean to SD ≈ 2.6

III > I > II

IMHO Option D

ermohit86 · Answer

sanjitscorps18 
Hi, How do you found Mean to SD ratio or SD? I know conventional method but is there any shortcut? I took approx 4 mins to solve the question so curious if any shortcut is available.

sanjitscorps18 · Answer

ermohit86

Not sure if this can be an actual GMAT question. The only way this may be possible would be if the mean of these lists are very close while the numbers are varying in their spread across the options or vice versa. In that scenario you can then get a fair idea of how the Mean to SD ratio would look like.

But with very different Means and varying ranges of SD it is difficult to create an estimate on the order in limited time. IMO at least one parameter (mean or SD) must be relatively close across the options so that the other one can be worked upon.

nousernamefine · Answer

Mean 65
SD=apx 11.XX
Ratio= 5.8 apx

Mean=42.5
SD=5.xx
Apx 7.xx

Mean=120
SD=22 apx
Ratio 5.3

Hence ans D

Arzeyone · Answer

I tried something simpler,

1) mean=65, diff between numbers = 10
2) mean=42.5, diff between numbers = 5
3) mean=120, diff between numbers = 20

now as this is an arithmetic progression, if say SD of (1) is x, then SD of (2) and (3) would change by the same factor as the diff between numbers change, so SD of (2) is (x/2) and that of (3) is (2x).

Now comparing ratios>> we have 65/x, 42.5/(x/2) and 120/(2x) simplifying we have 65/x, 85/x and 60/x for (1), (2) and (3) respectively. so the order would be (3)<(1)<(2), i.e., option D

Kinshook · Answer

Arrange the following sets in the order of the increasing magnitude of their mean to standard deviation ratio.

I. {50, 60, 70, 80}: 
Mean =  \frac{50+60+70+80}{4} = 65 ; 
Standard deviation =  \sqrt{\frac{15^2+5^2+5^2+15^2}{4}}=5\sqrt{5} = 11.2  ;
Mean/Standard Deviation =  \frac{65}{11.2}= 5.82

II. {35, 40, 45, 50}: 
Mean =  \frac{35+40+45+50}{4} = 42.5 ; 
Standard Deviation =  \sqrt{\frac{7.5^2+2.5^2+2.5^2+7.5^2}{4}}=5.6 ;
Mean/Standard Deviation =  \frac{42.5}{5.6} = 7.6

III. {90, 110, 130, 150}: 
Mean =  \frac{90+110+130+150}{4} = 120 ; 
Standard Deviation =  \sqrt{\frac{30^2+10^2+10^2+10^2}{4}}= 22.36  ; 
Mean/Standard Deviation =  \frac{120}{22.36} = 5.36

Since
III. (5.36) < I (5.82) < II (7.6)

A. I < II < III
B. II < III < I
C. II < I < III
D. III < I < II
E. III < II < I

IMO D

dhairya18 · Answer

To solve this comparison problem efficiently, avoid manual calculation of the standard deviation (SD). Instead, use the properties of scaling and spacing for symmetric sets.
 1. Find the Mean for each set
Since all three sets are symmetric (equal spacing between terms), the Mean is simply the average of the terms (the middle value).
 Set I: (50 + 60 + 70 + 80) / 4 = 65
 Set II: (35 + 40 + 45 + 50) / 4 = 42.5
 Set III: (90 + 110 + 130 + 150) / 4 = 120
 2. Compare the Standard Deviations (SD)
Standard deviation measures how far the numbers are spread from the mean.
 Set I vs Set II: Set I has a constant gap of 10 between terms, while Set II has a gap of 5. Because the gaps in Set I are exactly double those in Set II, the SD of Set I is twice the SD of Set II. (SD of I = 2 * SD of II).
 Set I vs Set III: Set III has a constant gap of 20, which is double the gap of 10 in Set I. Therefore, the SD of Set III is twice the SD of Set I. (SD of III = 2 * SD of I).
 The Relationship: If we let SD of II = S, then:
 SD of II = S
 SD of I = 2S
 SD of III = 4S
3. Calculate the Ratios (Mean / SD)
Now, plug the values into the ratio:
 * Ratio II: 42.5 / S = 42.5/S
 * Ratio I: 65 / 2S = 32.5/S
 * Ratio III: 120 / 4S = 30/S
4. Final Order
Comparing the values (30 < 32.5 < 42.5), the order of increasing magnitude is:
III < I < II
Correct Answer: D

Arrange the following sets in the order of the increasing magnitude of

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Arrange the following sets in the order of the increasing magnitude of

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