Respuesta :
Given the data set:
Journey Sample: 6, 5, 4, 5, 6, 4
Police Sample: 3, 8, 5, 1, 9, 4
Let's find the standard deviation of each sample.
• Standard deviation for Journey Sample.
First find the mean:
[tex]\begin{gathered} mean=\frac{sum\text{ of data}}{number\text{ of data}} \\ \\ mean=\frac{6+5+4+5+6+4}{6}=\frac{30}{6}=5 \end{gathered}[/tex]Now, apply the formula:
[tex]s=\sqrt{\frac{\Sigma(x-\mu)^2}{n-1}}[/tex]Where:
s is the standard deviation
x is the data
u is the mean
n is the number of data.
Thus, to find the standard deviation, we have:
[tex]\begin{gathered} s=\sqrt{\frac{(6-5)^2+(5-5)^2+(4-5)^2+(5-5)^2+(6-5)^2+(4-5)^2}{6-1}} \\ \\ s=\sqrt{\frac{(1)^2+(0)^2+(-1)^2+(0)^2+(1)^2+(-1)^2}{5}} \\ \\ s=\sqrt{\frac{1+1+1+1}{5}} \\ \\ s=\sqrt{\frac{4}{5}}=\sqrt{0.8}=0.9 \end{gathered}[/tex]Therefore, the standard deviation of the journey sample is 0.9
• Standard deviation of the Police sample.
Given the dataset: 3, 8, 5, 1, 9, 4
First find the mean:
[tex]mean=\frac{3+8+5+1+9+4}{6}=\frac{30}{6}=5[/tex]The mean is 5.
Now, to find the standard deviation, we have:
[tex]\begin{gathered} s=\sqrt{\frac{(3-5)^2+(8-5)^2+(5-5)^2+(1-5)^2+(9-5)^2+(4-5)^2}{6-1}} \\ \\ s=\sqrt{\frac{(-2)^2+(3)^2+(0)^2+(-4)^2+(4)^2+(-1)^2}{5}} \\ \\ s=\sqrt{\frac{4+9+16+16+1}{5}} \\ \\ s=\sqrt{\frac{46}{5}}=\sqrt{9.2}=3.03 \end{gathered}[/tex]Therefore, the standard deviation of the police sample is 3.03.
ANSWER:
• Standard deviation for the Journey Sample = 0.9
,• Standard deviation for the Police Sample = 3.03
