Question

(Lesson 9.1) (2 points)4. Now calculate the standard deviation for the Journey sample (6, 5, 4, 5, 6, 4) andThe Police sample (3, 8, 5, 1, 9, 4) separately below.Journey.The Police

Answer 1

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:

`\begin{gathered} mean=\frac{sum\text{ of data}}{number\text{ of data}} \\ \\ mean=(6+5+4+5+6+4)/(6)=(30)/(6)=5 \end{gathered}`

Now, apply the formula:

`s=\sqrt{(\Sigma(x-\mu)^2)/(n-1)}`

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:

`\begin{gathered} s=\sqrt{((6-5)^2+(5-5)^2+(4-5)^2+(5-5)^2+(6-5)^2+(4-5)^2)/(6-1)} \\ \\ s=\sqrt{((1)^2+(0)^2+(-1)^2+(0)^2+(1)^2+(-1)^2)/(5)} \\ \\ s=\sqrt{(1+1+1+1)/(5)} \\ \\ s=\sqrt{(4)/(5)}=√(0.8)=0.9 \end{gathered}`

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:

`mean=(3+8+5+1+9+4)/(6)=(30)/(6)=5`

The mean is 5.

Now, to find the standard deviation, we have:

`\begin{gathered} s=\sqrt{((3-5)^2+(8-5)^2+(5-5)^2+(1-5)^2+(9-5)^2+(4-5)^2)/(6-1)} \\ \\ s=\sqrt{((-2)^2+(3)^2+(0)^2+(-4)^2+(4)^2+(-1)^2)/(5)} \\ \\ s=\sqrt{(4+9+16+16+1)/(5)} \\ \\ s=\sqrt{(46)/(5)}=√(9.2)=3.03 \end{gathered}`

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