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GRE 1: Q160 V152
What is the resultant interquartile range for a set of unique positive
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24 Sep 2021, 07:19
24 Sep 2021, 07:19
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What is the resultant Inter-Quartile range for a set of unique positive values, if the values in the top 50-percentile are decreased by 3 and then divided by 5, while the values in the bottom 50 percentile (median included) are divided by 5 and then reduced by 3, given the original Inter-Quartile range was 48?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Source: Scholarden
p.s. I have spent 4-5 minutes trying to figure out and solve this question. It's an awesome one
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Source: Scholarden
p.s. I have spent 4-5 minutes trying to figure out and solve this question. It's an awesome one
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
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Location: India
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What is the resultant interquartile range for a set of unique positive
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28 Sep 2021, 11:12
28 Sep 2021, 11:12
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motion2020 wrote:
What is the resultant Inter-Quartile range for a set of unique positive values, if the values in the top 50-percentile are decreased by 3 and then divided by 5, while the values in the bottom 50 percentile (median included) are divided by 5 and then reduced by 3, given the original Inter-Quartile range was 48?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Source: Scholarden
p.s. I have spent 4-5 minutes trying to figure out and solve this question. It's an awesome one
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Source: Scholarden
p.s. I have spent 4-5 minutes trying to figure out and solve this question. It's an awesome one
Refer to the figure below;
Old IQR = \((x - y) = 48\)
New IQR = \(\frac{(x - 3)}{5} - (\frac{y}{5} - 3)\)
= \(\frac{x}{5} - \frac{y}{5} + 3 - \frac{3}{5}\)
= \(\frac{{(x - y) + 12}}{5} = \frac{{48 + 12}}{5} = \frac{60}{5} = 12\)
Hence, option C
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General Discussion
Moderator
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What is the resultant interquartile range for a set of unique positive
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19 Oct 2022, 09:04
19 Oct 2022, 09:04
Given that Original IQR (Inter-Quartile range) = 48
We know that IQR = \(Q_3\) - \(Q_1\) (Third Quartile - First Quartile) = 48
Now, all the values in the top 50% are decreased by 3 and then divided by 5
=> Value of \(Q_3\) which is also the middle value between \(Q_2\) and the highest value will also get decreased by 3 and then divided by 5
=> New \(Q_3\) = \(\frac{Q_3 - 3}{5}\) = \(\frac{Q_3}{5}\) - \(\frac{3}{5}\)
Now, all the values in the bottom 50% are divided by 5 and then reduced by 3
=> Value of \(Q_1\) which is also the middle value between Minimum value and \(Q_2\) will also get divided by 5 and then reduced by 3
=> New \(Q_1\) = \(\frac{Q_1}{5}\) - 3
=> New IQR = New \(Q_3\) - New \(Q_1\) = \(\frac{Q_3}{5}\) - \(\frac{3}{5}\) - (\(\frac{Q_1}{5}\) - 3)
= \(\frac{Q_3 - Q_1}{5}\) - \(\frac{3}{5}\) + 3
= \(\frac{48}{5}\) - \(\frac{3}{5}\) + 3
= \(\frac{48 - 3}{5}\) + 3
= 9 + 3 = 12
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Box and Whisker Plot
We know that IQR = \(Q_3\) - \(Q_1\) (Third Quartile - First Quartile) = 48
Now, all the values in the top 50% are decreased by 3 and then divided by 5
=> Value of \(Q_3\) which is also the middle value between \(Q_2\) and the highest value will also get decreased by 3 and then divided by 5
=> New \(Q_3\) = \(\frac{Q_3 - 3}{5}\) = \(\frac{Q_3}{5}\) - \(\frac{3}{5}\)
Now, all the values in the bottom 50% are divided by 5 and then reduced by 3
=> Value of \(Q_1\) which is also the middle value between Minimum value and \(Q_2\) will also get divided by 5 and then reduced by 3
=> New \(Q_1\) = \(\frac{Q_1}{5}\) - 3
=> New IQR = New \(Q_3\) - New \(Q_1\) = \(\frac{Q_3}{5}\) - \(\frac{3}{5}\) - (\(\frac{Q_1}{5}\) - 3)
= \(\frac{Q_3 - Q_1}{5}\) - \(\frac{3}{5}\) + 3
= \(\frac{48}{5}\) - \(\frac{3}{5}\) + 3
= \(\frac{48 - 3}{5}\) + 3
= 9 + 3 = 12
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Box and Whisker Plot
