Question

What is the standard deviation of the following set of data?

{21, 27, 29, 30, 31, 38, 41}

Answer 1

You can use the formula,
\[\sigma=\sqrt{\sum_{i=1}^n\frac{x_i^2}{n}-\overline{x}^2}\]
\[\overline{x}=\frac{21+ 27+ 29+ 30+ 31+ 38+ 41}{7}=31\]
So,
\[\sigma=\sqrt{\frac{21^2+ 27^2+ 29^2+ 30^2+ 31^2+ 38^2+ 41^2}{7}-31^2}\approx6.21\]

Answer 2

Can you help check a similar problem?
What is the standard deviation of the following set of data?

{3, 19, 27, 33, 46, 52}

I got 1168...

Answer 3

The formula I used before is the biased estimator of standard deviation. If you want the unbiased estimator. If we use again the biased estimator, then,
\[\overline{x}=30\]\[\sigma\approx16.37\]

Answer 4

ah okay

Answer 5

Also could you help with this one?
If a number cube is tossed twice, what is the probability that both rolls will display a number less than three?

Answer 6

The formula for the unbiased estimator of the standard deviation is,
\[\sigma=\sqrt{\sum_{i=1}^n\frac{(x_i-\overline{x})^2}{n-1}}\]
In this case, the above standard deviations would be,
\[\sigma_{unbiased}\approx 6.71\]
for the first problem, and,
\[\sigma_{unbiased}\approx 17.93\]
for the second.

Answer 7

For the problem of the cube, you have two independent experiments. So, the probabibility is,
2/6*2/6=4/36=1/9 (because the probability that one cube show a number less thatn 3 is 2/6).

Answer 8

Thank you so much. Those are my final answers? for the problems I asked? Thank you

Answer 9

You can put both, because there is two estimators. But if you don't know about unbiased estimators, then take the first answer.