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It is D. If mean=max value it means that all values are equal and STD deviation is 0

Should be B then?

I think that all you have to know about Standard deviation is that it is a measure of dispersion around the mean value.
If the range is 0, it means that MAX-MIN=0, or MAX value=Min Value. The deviation is obviously 0.
If the mean is = to MAX value, or = to the MIN value, then the set is composed of all equal numbers (nothing would have changed if the stem had said: "the least value is 5, and the mean is 5).
Hope it's sufficiently clear.

if range = 0, it does not mean that SD is necessarily 0.

5 values could be:

5,1,1,1,5 range = 0, but SD is not. 5,5,5,5,5 range = 0, SD = 0.

you're almost right.
In the first case, range is not 0, it is 4. (Max value is 5 and min value is 1)
In this case, range can be 0 only with all 5, as you say in your second example.

Last edited by thearch on 18 May 2005, 06:12, edited 1 time in total.

if range = 0, it does not mean that SD is necessarily 0.

5 values could be:

5,1,1,1,5 range = 0, but SD is not. 5,5,5,5,5 range = 0, SD = 0.

you're almost right. In the first case, range is not 0, it is 4. (Max value is 5 and min value is 1) In this case, range can be 0 only with -5 in the set, since 5 is the max value, or with all 5, as you say in your second example. But sales can't be negative, and the first option (with -5 in the set) is not possible.

I definately agree not only with the answer, but also the approach. nice explanation.

if range = 0, it does not mean that SD is necessarily 0.

5 values could be:

5,1,1,1,5 range = 0, but SD is not. 5,5,5,5,5 range = 0, SD = 0.

you're almost right. In the first case, range is not 0, it is 4. (Max value is 5 and min value is 1) In this case, range can be 0 only with [b]-5 in the set, since 5 is the max value[/b], or with all 5, as you say in your second example. But sales can't be negative, and the first option (with -5 in the set) is not possible.

I definately agree not only with the answer, but also the approach. nice explanation.

but i disagree with thearch's explanation that the range is zero if -5 is in the set. the only possible case to have zero is identical numbers.

if range = 0, it does not mean that SD is necessarily 0.

5 values could be:

5,1,1,1,5 range = 0, but SD is not. 5,5,5,5,5 range = 0, SD = 0.

you're almost right. In the first case, range is not 0, it is 4. (Max value is 5 and min value is 1) In this case, range can be 0 only with [b]-5 in the set, since 5 is the max value[/b], or with all 5, as you say in your second example. But sales can't be negative, and the first option (with -5 in the set) is not possible.

I definately agree not only with the answer, but also the approach. nice explanation.

but i disagree with thearch's explanation that the range is zero if -5 is in the set. the only possible case to have zero is identical numbers.

Yes, you're right of course. I wasn't referring to the -5 part, actually, I glossed over that. I was referring to the fact that you don't need to be able to calculate SD, you just have to know how to use it, and to understand what role range of 0 would have in a SD problem. It definately can come up on the real exam.

if range = 0, it does not mean that SD is necessarily 0.

5 values could be:

5,1,1,1,5 range = 0, but SD is not. 5,5,5,5,5 range = 0, SD = 0.

you're almost right. In the first case, range is not 0, it is 4. (Max value is 5 and min value is 1) In this case, range can be 0 only with [b]-5 in the set, since 5 is the max value[/b], or with all 5, as you say in your second example. But sales can't be negative, and the first option (with -5 in the set) is not possible.

I definately agree not only with the answer, but also the approach. nice explanation.

but i disagree with thearch's explanation that the range is zero if -5 is in the set. the only possible case to have zero is identical numbers.

Oh yes,
you're absolutely right, I think it is better to edit the post and delete such bulls**t

with statement 1 we already ahve the number 5 and we know that the highest value - the lowest is 0. So all number are equals. So deviation =0

with statement 2 we have the information that the mean is 5 but we only know one value for one month (5) so it can be 20,10,5,10,20 or 5,5,5,5,5 for example. Impossible to be sure of the deviation.

with statement 1 we already ahve the number 5 and we know that the highest value - the lowest is 0. So all number are equals. So deviation =0

with statement 2 we have the information that the mean is 5 but we only know one value for one month (5) so it can be 20,10,5,10,20 or 5,5,5,5,5 for example. Impossible to be sure of the deviation.

Hi antmavel,
probably you overlooked that the stem states that "During certain 5 months, the highest month sales value is 5"

with statement 1 we already ahve the number 5 and we know that the highest value - the lowest is 0. So all number are equals. So deviation =0

with statement 2 we have the information that the mean is 5 but we only know one value for one month (5) so it can be 20,10,5,10,20 or 5,5,5,5,5 for example. Impossible to be sure of the deviation.

Hi antmavel, probably you overlooked that the stem states that "During certain 5 months, the highest month sales value is 5"

1) The maimum value is 5 2) the remaining values su = 20 since there are 5 values 3) the only way that the remainng values can be = 20 is 5+5+5+5 since the max value is 5 4) if any one value is less than 5 then the remaining values one of them is greater than 5 example 4 6 5 5 5 -- 6 is not possible

so therefore answer is D

A is also Suff since if in a range al the values are equal only then the SD is 0

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