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Standard Deviation w/ OA

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by Stockmoose16 » Mon Nov 10, 2008 12:19 am
Can someone please explain this question?

The table shows the number of calls received by each of five operators during each of 4 one-hour periods. For which operator was the standard deviation of the numbers of calls received during these 4 periods the least?

Operator A: 3, 7, 7, 3
Operator B: 4, 5, 5, 6
Operator C: 8, 2, 5, 5
Operator D: 6, 4, 4, 6
Operator E: 3, 4, 5, 8

OA is B
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Re: Standard Deviation w/ OA

by logitech » Mon Nov 10, 2008 12:39 am
Stockmoose16 wrote:Can someone please explain this question?

The table shows the number of calls received by each of five operators during each of 4 one-hour periods. For which operator was the standard deviation of the numbers of calls received during these 4 periods the least?

Operator A: 3, 7, 7, 3
Operator B: 4, 5, 5, 6
Operator C: 8, 2, 5, 5
Operator D: 6, 4, 4, 6
Operator E: 3, 4, 5, 8

OA is B
SM16,

From Wikipedia, the free encyclopedia


In probability and statistics, the standard deviation is a measure of the dispersion of a collection of numbers. It can apply to a probability distribution, a random variable, a population or a data set. The standard deviation is usually denoted with the letter σ (lowercase sigma). It is defined as the root-mean-square (RMS) deviation of the values from their mean, or as the square root of the variance. Formulated by Galton in the late 1860s,[1] the standard deviation remains the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. If many data points are close to the mean, then the standard deviation is small; if many data points are far from the mean, then the standard deviation is large. If all data values are equal, then the standard deviation is zero. A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data.

Well - the more the terms are closer to the median , the smaller the SD

AV = Average ( by the way to make the calculation easy, the author designed the question so they all have the same average )

DIFF = # = AV

Operator A: 3, 7, 7, 3 AV :5 DIFF 2 2 2 2
Operator B: 4, 5, 5, 6 AV :5 DIFF 1 0 0 1
Operator C: 8, 2, 5, 5 AV :5 DIFF 3 3 0 0
Operator D: 6, 4, 4, 6 AV :5 DIFF 1 1 1 1
Operator E: 3, 4, 5, 8 AV :5 DIFF 2 1 0 3
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by vishubn » Mon Nov 10, 2008 12:43 am
Kewl !! Nice iNfo logitech !! thanks

Vishu
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by cramya » Mon Nov 10, 2008 5:57 am
The smaller the range the lower the standarad deviation

Operator B and D BOTH have the same range and in determing the lower of these 2 we need to look at the mean and the spread of the values around the mean. The mean being 5 operator B wins since it has 2 values which is the mean(20/4=5)

Hope this helps!
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by Ian Stewart » Mon Nov 10, 2008 10:48 am
cramya wrote:The smaller the range the lower the standarad deviation
That's not true. This set:

{1, 1, 1, 1, 1, 99, 99, 99, 99}

has a smaller range than this set:

{0, 50, 50, 50, 50, 50, 50, 100}

but the first set has a much larger standard deviation.
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by logitech » Mon Nov 10, 2008 11:02 am
Ian Stewart wrote:
cramya wrote:The smaller the range the lower the standarad deviation
That's not true. This set:

{1, 1, 1, 1, 1, 99, 99, 99, 99}

has a smaller range than this set:

{0, 50, 50, 50, 50, 50, 50, 100}

but the first set has a much larger standard deviation.
Cramya hope this helps. :)
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by cramya » Mon Nov 10, 2008 2:09 pm
That's not true. This set:

{1, 1, 1, 1, 1, 99, 99, 99, 99}

has a smaller range than this set:

{0, 50, 50, 50, 50, 50, 50, 100}

but the first set has a much larger standard deviation.
Ian,
Thanks for correcting me. Is it just the spread around the mean that determines the standard devaition i.e if its a samller list we can tell this by looking at the actual values like in this case but is there any startegy if its a larger list (may/may or not be on GMAT) but just to know?
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by Scott@TargetTestPrep » Tue Oct 15, 2019 6:36 pm
Stockmoose16 wrote:Can someone please explain this question?

The table shows the number of calls received by each of five operators during each of 4 one-hour periods. For which operator was the standard deviation of the numbers of calls received during these 4 periods the least?

Operator A: 3, 7, 7, 3
Operator B: 4, 5, 5, 6
Operator C: 8, 2, 5, 5
Operator D: 6, 4, 4, 6
Operator E: 3, 4, 5, 8

OA is B
We notice that the sum for each operator is 20; therefore, the mean number of calls for each operator is 5.

Since the standard deviation is a measure of how far data points are from the mean, we should look for the row with the values closest to 5.

Operator B has two calls equal to the mean, and two other calls that are pretty close to the mean. All the other operators either have no calls equal to the mean, or have other calls that are far away from the mean (or both). Thus, Operator B has the smallest standard deviation.

Answer: B

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by Scott@TargetTestPrep » Tue Oct 15, 2019 6:36 pm
Stockmoose16 wrote:Can someone please explain this question?

The table shows the number of calls received by each of five operators during each of 4 one-hour periods. For which operator was the standard deviation of the numbers of calls received during these 4 periods the least?

Operator A: 3, 7, 7, 3
Operator B: 4, 5, 5, 6
Operator C: 8, 2, 5, 5
Operator D: 6, 4, 4, 6
Operator E: 3, 4, 5, 8

OA is B
We notice that the sum for each operator is 20; therefore, the mean number of calls for each operator is 5.

Since the standard deviation is a measure of how far data points are from the mean, we should look for the row with the values closest to 5.

Operator B has two calls equal to the mean, and two other calls that are pretty close to the mean. All the other operators either have no calls equal to the mean, or have other calls that are far away from the mean (or both). Thus, Operator B has the smallest standard deviation.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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