Answer:
So, the sample standard deviation is 7.1.
Step-by-step 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:
[tex]\sigma=\sqrt{\frac{1}{N-1}\cdot \sum_{i=1}^{N} (x_i-\mu)^2[/tex]
So, μ is the mean of all our values.
We get:
[tex]\mu=\frac{2+6+15+9+11+22+1+4+8+19}{10}\\\\\mu=\frac{97}{10}\\\\\mu=9.7[/tex]
Now, we calculate the sum
[tex]\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[/tex]
Therefore, we get
[tex]\sigma=\sqrt{\frac{1}{N-1}\cdot \sum_{i=1}^{N} (x_i-\mu)^2}\\\\\sigma=\sqrt{\frac{1}{10-1}\cdot 452.1}\\\\\sigma=7.087\\\\\sigma=7.1\\[/tex]
So, the sample standard deviation is 7.1.
