Chapter 11.1, Problem 24E

(a)

To determine

To find the Standard Deviation of Rookie Season.

Answer to Problem 24E

Standard Deviation = $2.08$

Explanation of Solution

Given information: $1,0,6,2,0,3$

Formula Used: Standard Deviation = $\sqrt{\frac{\sum {\left(\left|x_i-\mu \right|\right)}^2}{N}}$ and Mean $\mu =\frac{Sumofallobservations}{Totalobservations}$

Calculation:

  $1,0,6,2,0,3$

Now, in Ascending Order

  $0,0,1,2,3,6$

• Mean

Mean = $\frac{Sumofallobservations}{Totalobservations}$

So,

Mean = $\frac{0+0+1+2+3+6}{6}$

Now,

Mean = $\frac{12}{6}$

Hence,

Mean $\mu =2$

• Standard Deviation

  $x_i=0,0,1,2,3,6$

and

Mean $\mu =2$

So,

  $\left|x_i-\mu \right|=2,2,1,0,1,4$

Now,

  ${\left(\left|x_i-\mu \right|\right)}^2=4,4,1,0,1,16$

So,

Standard Deviation = $\sqrt{\frac{\sum {\left(\left|x_i-\mu \right|\right)}^2}{N}}$

Now,

Standard Deviation = $\sqrt{\frac{4+4+1+0+1+16}{6}}$

So,

Standard Deviation = $\sqrt{\frac{26}{6}}$

Now,

Standard Deviation = $\sqrt{4.33}$

Hence,

Standard Deviation = $2.08$

(b)

To determine

To find the Standard Deviation of This Season.

Answer to Problem 24E

Standard Deviation = $3.06$

Explanation of Solution

Given information: $4,6,4,8,7,13$

Formula Used: Standard Deviation = $\sqrt{\frac{\sum {\left(\left|x_i-\mu \right|\right)}^2}{N}}$ and Mean $\mu =\frac{Sumofallobservations}{Totalobservations}$

Calculation:

  $4,6,4,8,7,13$

Now, in Ascending Order

  $4,4,6,7,8,13$

• Mean

Mean = $\frac{Sumofallobservations}{Totalobservations}$

So,

Mean = $\frac{4+4+6+7+8+13}{6}$

Now,

Mean = $\frac{42}{6}$

Hence,

Mean $\mu =7$

• Standard Deviation

  $x_i=4,4,6,7,8,13$

and

Mean $\mu =7$

So,

  $\left|x_i-\mu \right|=3,3,1,0,1,6$

Now,

  ${\left(\left|x_i-\mu \right|\right)}^2=9,9,1,0,1,36$

So,

Standard Deviation = $\sqrt{\frac{\sum {\left(\left|x_i-\mu \right|\right)}^2}{N}}$

Now,

Standard Deviation = $\sqrt{\frac{9+9+1+0+1+36}{6}}$

So,

Standard Deviation = $\sqrt{\frac{56}{6}}$

Now,

Standard Deviation = $\sqrt{9.33}$

Hence,

Standard Deviation = $3.06$

(c)

To determine

Compare the Standard Deviation of Rookie Season and This Season.

Answer to Problem 24E

Standard Deviation of Rookie Season < Standard Deviation of This Season

Explanation of Solution

Given information: Standard Deviation of Rookie Season = $2.08$ and Standard Deviation of This Season = $3.06$

Formula Used: Compatibility

Calculation:

Standard Deviation of Rookie Season = $2.08$ and Standard Deviation of This Season = $3.06$

Hence, compare

Standard Deviation of Rookie Season < Standard Deviation of This Season