Question

How do I find a standard deviation?

Answer 1

For sample standard deviation,$$s^2=\frac1n\sum_i^n(x_i-\bar{x})^2$$

Answer 2

\[s = \sqrt{\frac{ \sum_{(x - x _{1})^2} }{ n-1 }}\]

wehere s = stanard deviation, x = all values in data set, x1 = each value in the data set, and n = number of values in the data set.

Answer 3

oh my, lol that's all confusing. So if the data set is {72, 76, 84, 90, 93, 95}, n will be 6, and what will x and x1 be?

Answer 4

x would be any value, and x1 would be the mean. so find the mean of all 6 numbers, and then take each individual number and subtract the mean, then square it

Answer 5

and then the summation symbol means you'll do each number that way and find the sum. so (72 - (mean))^2 + (76 - (mean))^2, so on and so forth

Answer 6

oh! okey dokey (: thank you!

Answer 7

\[\begin{array}{c|c|c} x & x-\overline{x} & (x-\overline{x})^2\\\hline72 &72-85=-13&(-13)^2=169\\76&-9&81\\84& -1&1\\90&5&25\\93&8&64\\95&10&100\\\hline510&0&440\end{array}\]

Answer 8

you're welcome! if you need more help figuring it out, heres the easy way\[(72 - 85)^2 + (76 - 85)^2 + (84 - 85)^2 + (90 - 85)^2 + (93 - 85)^2 + (95 - 85)^2\]
then divide by 5
\[440 \div 5=s\]

Answer 9

\[440 \div 5=s^2\]

Answer 10

yes, s^2. forgot the exponent!

Answer 11

another way is to compute

\[s=\sqrt{\frac{n\displaystyle\sum_{i=1}^{n}x_i^2-\left(\sum_{i=1}^{n}x_1\right)^2}{n(n-1)}}\]

Answer 12

wait, is it s^2? i checked with a standard deviation calculator online and the answer was 88, which was my answer before squaring.

Answer 13

\[s=\sqrt{\frac{n\displaystyle\sum_{i=1}^{n}x_i^2-\left(\sum_{i=1}^{n}x_i\right)^2}{n(n-1)}}\]

small typo..had a 1 and not an \(i\)

Answer 14

88 is the variance

Answer 15

right, my mistake. thanks!