mean and dtandard deviation

[manikdhingra]

9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5
The mean and the standard deviation of the 8 numbers shown are 10 and 0.3, respectively. what percentage of the 8 number's are within 1 standard deviation?
A) 90% B) 85% C) 80% D) 75% E) 70%

please explain if some straight forward formula is involved....m weak in statistics

[Meggieski]

You need to memorize this: 34,14,2. 68% falls within one SD, another 28 within 2 SD and the remainder in 3 SD (100%)

If the ranges are 9.7 and 10.3, then 6 of the 8 fall within 1SD. 6/8 is the same as 75%.

[suwarnapatel]

6/8 = 3/4 = 75%

Mean = 10
SD = 0.3

Range of 1 SD 9.7 to 10.3 (add and sub SD from mean)

There are 6 values that fall in this range
6/8 = 75%


Meggieski, please explain your answer a bit; what is it that we need to memorize?

[suwarnapatel]

You really know your stats... I just figured what you were trying to say:

I guess when data is normally distributed, 68% falls under 1SD from the mean. 95% 2 SD & 99% within 3 SD

Wow! OK! Now I know this.....

[Meggieski]

Yeah.

According to my PR teacher, the only thing they will test is your knowledge of the normal distribution curve percentages. Just memorize 34, 14, 2 or 68,28,4 and youre good to go.

Sometimes it helps to draw out the curve and put it on your study sheet. Visual images always help me the most. Also, the "variance" is the same thing as saying the entire range of 1sd 2sd etc.. If you are thinking variance think 68, 28, 4.. if just SD think the 34,14,2.

[flex_manny]

Meggieski:

I am still unclear with your explanation. if you are talking Normal distribution, then how would that generalization apply here. Can you explain once more how you applied your logic ( and what the logic is )

Thanks

[suwarnapatel]

You know about distributions and Bell Curves right?
Now apparently, it is a proven fact that all values in a normal distribution fall under the following table:

Within 1 SD : 68% of the values of the distribution
Within 2 SD : 96% of the values of the distribution
Within 3 SD : 98% of the values of the distribution

Between 1 and 2 SD per Meggiski: 96-68=28%
Between 2 abd 3 SD = 4% 98.8-96 = 4%

Check this out:
The bell curve & standard deviation
Populations

[GmatG]

Originally Posted by Meggieski

You need to memorize this: 34,14,2. 68% falls within one SD, another 28 within 2 SD and the remainder in 3 SD (100%)

If the ranges are 9.7 and 10.3, then 6 of the 8 fall within 1SD. 6/8 is the same as 75%.

Agree completely with Meggieski

[Makumajon]

Hi, the rule that Meggieski mentioned applies only to Normal Distribution. Unless you are certain about the data distribution, you must NOT apply that. For the present problem, it is not necessary at all to memorize 34, 14 rule. Applying this rule may even lead to wrong result. Suwarna's fundamental method is right for this problem.

[bose]

find the number of values that fall in 1 SD i.e range 9.7 to 10.3,= 6
now % of #s in 1 SD is 6/8=75%