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rxs0005
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Standard deviation clarification 05 Apr 2011, 16:04
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If A = { 2 , 4 , 6, 8 }

B = { 14, 21, 28, 35 }


even though A and B are evenly spaced the SD of A < SD of B right ?

will this change if the number of terms are changed in the sets



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Standard deviation clarification 06 Apr 2011, 18:11
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rxs0005
If A = { 2 , 4 , 6, 8 }

B = { 14, 21, 28, 35 }


even though A and B are evenly spaced the SD of A < SD of B right ?

will this change if the number of terms are changed in the sets
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SD is a measure of dispersion around the mean i.e. how are the numbers distributed around the mean. The dispersion is 0 if all the numbers are equal to mean itself. The farther away the numbers are from the mean, the higher is the dispersion and hence, higher is the SD. For a qualitative comparison, if confusion arises, draw them on a number line.

Attachment:
Ques2.jpg
Ques2.jpg [ 10.67 KiB | Viewed 3044 times ]
We see above that in the first figure the numbers are closer together than in the second one so SD of the first set is smaller than the SD of the second set. Similarly, if you add more numbers (as shown in the third figure), the dispersion increases and hence the SD of the third set is greater than that of the first set. Now, would you like to guess about the SD of the second set compared to the SD of the third set above?
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Standard deviation clarification 12 Apr 2011, 11:03
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VeritasPrepKarishma

Now, would you like to guess about the SD of the second set compared to the SD of the third set above?
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I guess the answer is SD(second) > SD (third). Pls can you shed some light on the range of the data - I made two observations about the third set -
a. the third set has more numbers. So this decreases the SD.
b. the widest data is 5 units away from mean

whereas third set has less numbers and the widest data is 10.5 units away from the mean.

If the sets had equal #numbers then wouldn't range decide the SD - more range is equivalent to more deviation.
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Standard deviation clarification 12 Apr 2011, 18:30
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I guess the answer is SD(second) > SD (third). Pls can you shed some light on the range of the data - I made two observations about the third set -
a. the third set has more numbers. So this decreases the SD.
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Actually, you generally cannot decide anything based on how many numbers there are. e.g if a set has 4 numbers, all very far from each other and another set has 3 numbers very close to each other, the SD of the set with 3 numbers will be smaller. The point is how dispersed the numbers are.

In the diagram above, in the second set, the numbers are far away from each other. In the third set, the numbers are closer to each other. Hence SD of second set > SD of third set.

If there are two sets A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6}, here SD of B > SD of A. The reason again is not directly linked to the fact that B has more numbers. SD of B is higher because it has numbers that are farther away from the mean. The mean of B is 3.5 and numbers 1 and 6 are 2.5 away from the mean. In set A, the extreme terms are only 1.5 away from the mean.

There are cases where just the number of terms could decide the SD. e.g.
A = {1, 1, 3, 5, 5}, B = {1, 3, 5}
Here, there are more terms which are far from the mean hence SD of A > SD of B

My suggestion would be to plot the numbers on the number line, mark the mean there and see in which set the values are more dispersed from the mean. The values will be such that you will get a very clear idea.
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Standard deviation clarification 12 Apr 2011, 21:44
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Thanks Karishma !!



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