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# A certain list of 100 data has an average (arithmetic mean) of 6 and

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Re: A certain list of 100 data has an average (arithmetic mean) of 6 and [#permalink]
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I agree with sriharimurthy.
In most cases Standard Deviation question can be solved without using SD formula.
The main idea is to think of SD as of average deviation from mean: $$average (|x - x_{av}|)$$.
So, 6 and 6 add two 0s in average formula and must reduce SD.
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Re: A certain list of 100 data has an average (arithmetic mean) of 6 and [#permalink]
Hi Sriharimurthy,
thats a great explanation,but i am stuck with one point.
when u r calculating the new SD.how can u subtract 6 hrom both x and y??6 is the mean of the old set...for examle if u add 0 and 0 the new mean will be 600/102.ie,will be less than 6. the mean will change as well..
Kindly explain this point...will really appriciate..
Thanx
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Re: A certain list of 100 data has an average (arithmetic mean) of 6 and [#permalink]
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Gmatter111 wrote:
A certain list of 100 data has an average (arithmetic mean) of 6 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 102 data with standard deviation less than d?

A. -6 and 0
B. 0 and 0
C. 0 and 6
D. 0 and 12
E. 6 and 6

Thanks!

We should keep in mind that the closer the data points are to the mean, the “lower” the standard deviation. Thus, since the mean is 6, when we add two additional values of 6 to the data set, the standard deviation will decrease.

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Re: A certain list of 100 data has an average (arithmetic mean) of 6 and [#permalink]
I have prepared a youtube video to explain this question. Hope you'll like it.

Check the explanation on this video
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Re: A certain list of 100 data has an average (arithmetic mean) of 6 and [#permalink]
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Re: A certain list of 100 data has an average (arithmetic mean) of 6 and [#permalink]
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