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There are a lot of products. Is the standard deviation of the prices o

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MathRevolution
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There are a lot of products. Is the standard deviation of the prices o [#permalink] New post   21 Apr 2017, 01:27
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Question Stats:

38% (01:15) correct 62% (01:21) wrong based on 111 sessions
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There are a lot of products. Is the standard deviation of the prices of the products less than $60?

1) The median value of their price is $100
2) The range of their price is $110
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B
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ganand
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Re: There are a lot of products. Is the standard deviation of the prices o [#permalink] New post   21 Apr 2017, 23:58
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VyshakhR1995 wrote:
I am Not sure whether i am Right....There a rule suggesting STD Should be approximately equal to One fourth the value of the range...

Here Range is 110 So STD will be less than 60...
statement 1 tells next to nothing..

Hence B


Hi VyshakhR1995,

To be precise Standard deviation of any data set will always be less than equal to Range/2.

I'll demonstrate it with a small example.

consider two numbers 6 and 10.

1. Find the mean. (6+10)/2 = 8

2. Take the difference from the mean. 8 - 6 = 2 , 10 - 8 = -2

3. Square the difference. 2^2 = 4, (-2)^2 = 4

4. Take the mean of the squares of the difference from the mean. => (4+ 4)/2 = 4

5. Take the square root of step 4 result. => \(\sqrt{4} = 2\)

Standard deviation = 2

Range = 10 - 6 = 4 .

In this case, SD is equal to Range/2.

But if you insert any other element within this range, then SD will further decrease.

=> Standard deviation <= Range/2

Thanks.
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Re: There are a lot of products. Is the standard deviation of the prices o [#permalink] New post   24 Apr 2017, 02:46
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==> If you modify the original condition and the question, you get standard deviation(d)≤range/2. Then, from d≤range/2=$110/2=$55<$60, it is always yes and sufficient.

Therefore, the answer is B.
Answer: B
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Re: There are a lot of products. Is the standard deviation of the prices o [#permalink] New post   21 Apr 2017, 20:56
I am Not sure whether i am Right....There a rule suggesting STD Should be approximately equal to One fourth the value of the range...

Here Range is 110 So STD will be less than 60...
statement 1 tells next to nothing..

Hence B
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Re: There are a lot of products. Is the standard deviation of the prices o [#permalink] New post   05 Jan 2023, 10:44
Hi MathRevolution,

Can you confirm if the formula is Range/2 or Range/4? Some external websites say that the formula is the latter.

TIA
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Re: There are a lot of products. Is the standard deviation of the prices o [#permalink]
05 Jan 2023, 10:44
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Bunuel
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