Chapter 11.1, Problem 20E

(a)

To determine

To find the Range.

Answer to Problem 20E

Range = $25$

Explanation of Solution

Given information: $141,116,117,135,126,121$

Formula Used: Range = Highest − Lowest

Calculation:

  $141,116,117,135,126,121$

So, In Ascending Order

  $116,117,121,126,135,141$

Now,

Range = Highest − Lowest

So,

Range = $141-116$

Hence,

Range = $25$

(b)

To determine

To find the Standard Deviation.

Answer to Problem 20E

Standard Deviation = $9.24$

Explanation of Solution

Given information: $141,116,117,135,126,121$

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

Calculation:

  $141,116,117,135,126,121$

Now, in Ascending Order

  $116,117,121,126,135,141$

• Mean

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

So,

Mean = $\frac{116+117+121+126+135+141}{6}$

Now,

Mean = $\frac{756}{6}$

Hence,

Mean $\mu =126$

• Standard Deviation

  $x_i=116,117,121,126,135,141$

and

Mean $\mu =126$

So,

  $\left|x_i-\mu \right|=10,9,5,0,9,15$

Now,

  ${\left(\left|x_i-\mu \right|\right)}^2=100,81,25,0,81,225$

So,

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

Now,

Standard Deviation = $\sqrt{\frac{100+81+25+0+81+225}{6}}$

So,

Standard Deviation = $\sqrt{\frac{512}{6}}$

Now,

Standard Deviation = $\sqrt{85.33}$

Hence,

Standard Deviation = $9.24$