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The data sets I, II, and III above are ordered from greatest standard

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Bunuel
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The data sets I, II, and III above are ordered from greatest standard [#permalink] New post   16 Jul 2021, 07:45
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00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

78% (00:57) correct 22% (01:00) wrong based on 63 sessions
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I. 14.82, 14.82, 14.82, 14.82, 14.82
II. 13.22, 14.82, 14.82, 14.82, 16.12
III. 14.62, 14.72, 14.82, 14.92, 15.02

The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following?

A I, III, II
B II, I, III
C II, III, I
D III, I, II
E III, II, I
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C
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Re: The data sets I, II, and III above are ordered from greatest standard [#permalink] New post   16 Jul 2021, 08:42
14.82 is the median for all sets

in set 1 all terms are equal, hence SD = 0 ; least
in set 2 13.22 and 16.12 are further away from median; hence SD is largest compared to set 3, which is clustered around median more closely
hence 2,3,1 is the sequence
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Re: The data sets I, II, and III above are ordered from greatest standard [#permalink] New post   16 Jul 2021, 09:06
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Solution:

There can be a methodical way of solving this. Where we solve for SD in each case and get our answer. But that would be too cumbersome.

Inference Approach:

Standard Deviation is the measure of how much data is scattered.

On looking we can say that SD of Data set \(I\) is 0. because all the elements in that data \(14.82, 14.82, 14.82, 14.82, 14.82\) are the same. The data is not scattered at all.

Coming to Data set \(II\). The elements in this set is a little scattred \(13.22, 14.82, 14.82, 14.82, 16.12\). The smallest being \(13.22\) and largest \(16.12\).

Data set \(III\): the smallest in this is \(14.62\) and the largest is \(15.02\).

We can very clearly see that data in \(II\) is more scattered than \(I\).

Thus the correct order is \(II, III, I\).

Hence the right answer is Option C.
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Re: The data sets I, II, and III above are ordered from greatest standard [#permalink] New post   16 Jul 2021, 09:20
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As data values are the same in Set I, S.D. = 0.

We need the arrangement from greatest to least so Set I will be third place. So, either Option C or E is the answer.

Set III has less spread of data around mean [14.82 - 14.62 = 0.2 and 15.02 - 14.82 = 0.2]

Asnwer C
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Re: The data sets I, II, and III above are ordered from greatest standard [#permalink] New post   21 Jul 2021, 08:20
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Theory: Standard Deviation (SD) is an indication of how spread the numbers are as compared to the Mean

SET I. 14.82, 14.82, 14.82, 14.82, 14.82
Theory: If all numbers in the set are same then the SD=0

SET II. 13.22, 14.82, 14.82, 14.82, 16.12
Numbers 13.22 and 16.12 looks too far from 14.xx something, so SD will be BIG for this set

SET III. 14.62, 14.72, 14.82, 14.92, 15.02
Numbers 14.62 and 15.02 looks NOT so far from 14.xx something, so SD will be smaller than Set II,

=> SD of II > III > I

So, Answer will be C
Hope it helps!

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Re: The data sets I, II, and III above are ordered from greatest standard [#permalink] New post   16 Sep 2021, 02:58
Just find the range of each data and then find the greatest to the lowest.
Range works when each data set have the same number of entries.

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Re: The data sets I, II, and III above are ordered from greatest standard [#permalink]
16 Sep 2021, 02:58
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