Question

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. 2, 6, 15, 9, 11, 22, 1, 4, 8,19

A. 6.3
B. 7.1
C. 6.8
D. 2.1

Answer 1

So, the sample standard deviation is 7.1.

Explanation:

From Exercise we have the next numbers: 2, 6, 15, 9, 11, 22, 1, 4, 8,19.

So, N=10, because we have 10 numbers.

We use the formula for standard deviation:

`\sigma=\sqrt{(1)/(N-1)\cdot \sum_(i=1)^(N) (x_i-\mu)^2`

So, μ is the mean of all our values.

We get:

`\mu=(2+6+15+9+11+22+1+4+8+19)/(10)\\\\\mu=(97)/(10)\\\\\mu=9.7`

Now, we calculate the sum

`\sum_(i=1)^(10) (x_i-9.7)^2=(2-9.7)^2+(6-9.7)^2+(15-9.7)^2+(9-9.7)^2+(11-9.7)^2+(22-9.7)^2+(1-9.7)^2+(4-9.7)^2+(8-9.7)^2+(19-9.7)^2\\\\\sum_(i=1)^(10) (x_i-9.7)^2=452.1`

Therefore, we get

`\sigma=\sqrt{(1)/(N-1)\cdot \sum_(i=1)^(N) (x_i-\mu)^2}\\\\\sigma=\sqrt{(1)/(10-1)\cdot 452.1}\\\\\sigma=7.087\\\\\sigma=7.1\\`

So, the sample standard deviation is 7.1.