Find the range .

Question

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Answer 1

Question

Chapter 3.2, Problem 13P

a.

To determine

Find the range.

a.

Expert Solution

Answer to Problem 13P

The range is 15.

Explanation of Solution

The range is obtained below:

$Range=Largest value−Smallest value=30−15=15$

Thus, the range is 15.

b.

To determine

Verify that $∑x=110$ and $∑x2=2568$ using calculator.

b.

Expert Solution

Explanation of Solution

Step-by-step procedure to verify $∑x=110$ and $∑x2=2568$ using Ti83 calculator:

Press STAT.
Select Edit.
Enter the values in L1.
Press STAT and Choose CALC.
Select 1-Var Stats.
To select the variable L1, Press 2-nd and then press 1.
Press Enter.

Output obtained using the Ti83 calculator is given below:

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 3.2, Problem 13P

From the output, the values of $∑x=110$ and $∑x2=2,568$ .

c.

To determine

Find the sample variance and the sample standard deviation using the computation formula.

c.

Expert Solution

Answer to Problem 13P

The sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is 6.08.

Explanation of Solution

The sample variance using the computation formula is given below:

$s2=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the computation formula is given below:

$s=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample variance using the computation formula is obtained below:

$s2=2,568−(110)255−1=37$

Thus, the sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is obtained below:

$s=2,568−(110)255−1=37=6.08$

Thus, the sample standard deviation using the computation formula is 6.08.

d.

To determine

Find the sample variance using the defining formula.

Find the sample standard deviation using the defining formula.

d.

Expert Solution

Answer to Problem 13P

The sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is 6.08.

Explanation of Solution

The sample variance using the defining formula is given below:

$s2=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the defining formula is given below:

$s=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The value of $x¯$ is obtained below:

$x¯=∑xn=23+17+15+30+255=22$

The value of $∑(x−x¯)2$ is obtained below:

x	$x−x¯$	$(x−x¯)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−x¯)2=148$

The sample variance using the defining formula is given below:

$s2=1485−1=1484=37$

Thus, the sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is given below:

$s=1485−1=1484=6.08$

Thus, the sample standard deviation using the defining formula is 6.08.

e.

To determine

Find the population variance using the defining formula.

Find the population standard deviation using the defining formula.

e.

Expert Solution

Answer to Problem 13P

The population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is 5.44.

Explanation of Solution

The population variance using the defining formula is given below:

$σ2=∑(x−μ)2n$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The population standard deviation using the defining formula is given below:

$σ=∑(x−μ)2N$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The value of $μ$ is obtained below:

$μ=∑xN=23+17+15+30+255=22$

The value of $∑(x−μ)2$ is obtained below:

x	$x−μ$	$(x−μ)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−μ)2=148$

The population variance using the defining formula is given below:

$σ2=1485=29.6$

Thus, the population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is given below:

$σ=1485=5.44$

Thus, the population standard deviation using the defining formula is 5.44.

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Answer 2

Question

Chapter 3.2, Problem 13P

a.

To determine

Find the range.

a.

Expert Solution

Answer to Problem 13P

The range is 15.

Explanation of Solution

The range is obtained below:

$Range=Largest value−Smallest value=30−15=15$

Thus, the range is 15.

b.

To determine

Verify that $∑x=110$ and $∑x2=2568$ using calculator.

b.

Expert Solution

Explanation of Solution

Step-by-step procedure to verify $∑x=110$ and $∑x2=2568$ using Ti83 calculator:

Press STAT.
Select Edit.
Enter the values in L1.
Press STAT and Choose CALC.
Select 1-Var Stats.
To select the variable L1, Press 2-nd and then press 1.
Press Enter.

Output obtained using the Ti83 calculator is given below:

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 3.2, Problem 13P

From the output, the values of $∑x=110$ and $∑x2=2,568$ .

c.

To determine

Find the sample variance and the sample standard deviation using the computation formula.

c.

Expert Solution

Answer to Problem 13P

The sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is 6.08.

Explanation of Solution

The sample variance using the computation formula is given below:

$s2=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the computation formula is given below:

$s=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample variance using the computation formula is obtained below:

$s2=2,568−(110)255−1=37$

Thus, the sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is obtained below:

$s=2,568−(110)255−1=37=6.08$

Thus, the sample standard deviation using the computation formula is 6.08.

d.

To determine

Find the sample variance using the defining formula.

Find the sample standard deviation using the defining formula.

d.

Expert Solution

Answer to Problem 13P

The sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is 6.08.

Explanation of Solution

The sample variance using the defining formula is given below:

$s2=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the defining formula is given below:

$s=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The value of $x¯$ is obtained below:

$x¯=∑xn=23+17+15+30+255=22$

The value of $∑(x−x¯)2$ is obtained below:

x	$x−x¯$	$(x−x¯)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−x¯)2=148$

The sample variance using the defining formula is given below:

$s2=1485−1=1484=37$

Thus, the sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is given below:

$s=1485−1=1484=6.08$

Thus, the sample standard deviation using the defining formula is 6.08.

e.

To determine

Find the population variance using the defining formula.

Find the population standard deviation using the defining formula.

e.

Expert Solution

Answer to Problem 13P

The population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is 5.44.

Explanation of Solution

The population variance using the defining formula is given below:

$σ2=∑(x−μ)2n$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The population standard deviation using the defining formula is given below:

$σ=∑(x−μ)2N$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The value of $μ$ is obtained below:

$μ=∑xN=23+17+15+30+255=22$

The value of $∑(x−μ)2$ is obtained below:

x	$x−μ$	$(x−μ)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−μ)2=148$

The population variance using the defining formula is given below:

$σ2=1485=29.6$

Thus, the population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is given below:

$σ=1485=5.44$

Thus, the population standard deviation using the defining formula is 5.44.

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Answer 3

Question

Chapter 3.2, Problem 13P

a.

To determine

Find the range.

a.

Expert Solution

Answer to Problem 13P

The range is 15.

Explanation of Solution

The range is obtained below:

$Range=Largest value−Smallest value=30−15=15$

Thus, the range is 15.

b.

To determine

Verify that $∑x=110$ and $∑x2=2568$ using calculator.

b.

Expert Solution

Explanation of Solution

Step-by-step procedure to verify $∑x=110$ and $∑x2=2568$ using Ti83 calculator:

Press STAT.
Select Edit.
Enter the values in L1.
Press STAT and Choose CALC.
Select 1-Var Stats.
To select the variable L1, Press 2-nd and then press 1.
Press Enter.

Output obtained using the Ti83 calculator is given below:

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 3.2, Problem 13P

From the output, the values of $∑x=110$ and $∑x2=2,568$ .

c.

To determine

Find the sample variance and the sample standard deviation using the computation formula.

c.

Expert Solution

Answer to Problem 13P

The sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is 6.08.

Explanation of Solution

The sample variance using the computation formula is given below:

$s2=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the computation formula is given below:

$s=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample variance using the computation formula is obtained below:

$s2=2,568−(110)255−1=37$

Thus, the sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is obtained below:

$s=2,568−(110)255−1=37=6.08$

Thus, the sample standard deviation using the computation formula is 6.08.

d.

To determine

Find the sample variance using the defining formula.

Find the sample standard deviation using the defining formula.

d.

Expert Solution

Answer to Problem 13P

The sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is 6.08.

Explanation of Solution

The sample variance using the defining formula is given below:

$s2=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the defining formula is given below:

$s=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The value of $x¯$ is obtained below:

$x¯=∑xn=23+17+15+30+255=22$

The value of $∑(x−x¯)2$ is obtained below:

x	$x−x¯$	$(x−x¯)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−x¯)2=148$

The sample variance using the defining formula is given below:

$s2=1485−1=1484=37$

Thus, the sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is given below:

$s=1485−1=1484=6.08$

Thus, the sample standard deviation using the defining formula is 6.08.

e.

To determine

Find the population variance using the defining formula.

Find the population standard deviation using the defining formula.

e.

Expert Solution

Answer to Problem 13P

The population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is 5.44.

Explanation of Solution

The population variance using the defining formula is given below:

$σ2=∑(x−μ)2n$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The population standard deviation using the defining formula is given below:

$σ=∑(x−μ)2N$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The value of $μ$ is obtained below:

$μ=∑xN=23+17+15+30+255=22$

The value of $∑(x−μ)2$ is obtained below:

x	$x−μ$	$(x−μ)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−μ)2=148$

The population variance using the defining formula is given below:

$σ2=1485=29.6$

Thus, the population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is given below:

$σ=1485=5.44$

Thus, the population standard deviation using the defining formula is 5.44.

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Answer 4

Question

Chapter 3.2, Problem 13P

a.

To determine

Find the range.

a.

Expert Solution

Answer to Problem 13P

The range is 15.

Explanation of Solution

The range is obtained below:

$Range=Largest value−Smallest value=30−15=15$

Thus, the range is 15.

b.

To determine

Verify that $∑x=110$ and $∑x2=2568$ using calculator.

b.

Expert Solution

Explanation of Solution

Step-by-step procedure to verify $∑x=110$ and $∑x2=2568$ using Ti83 calculator:

Press STAT.
Select Edit.
Enter the values in L1.
Press STAT and Choose CALC.
Select 1-Var Stats.
To select the variable L1, Press 2-nd and then press 1.
Press Enter.

Output obtained using the Ti83 calculator is given below:

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 3.2, Problem 13P

From the output, the values of $∑x=110$ and $∑x2=2,568$ .

c.

To determine

Find the sample variance and the sample standard deviation using the computation formula.

c.

Expert Solution

Answer to Problem 13P

The sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is 6.08.

Explanation of Solution

The sample variance using the computation formula is given below:

$s2=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the computation formula is given below:

$s=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample variance using the computation formula is obtained below:

$s2=2,568−(110)255−1=37$

Thus, the sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is obtained below:

$s=2,568−(110)255−1=37=6.08$

Thus, the sample standard deviation using the computation formula is 6.08.

d.

To determine

Find the sample variance using the defining formula.

Find the sample standard deviation using the defining formula.

d.

Expert Solution

Answer to Problem 13P

The sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is 6.08.

Explanation of Solution

The sample variance using the defining formula is given below:

$s2=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the defining formula is given below:

$s=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The value of $x¯$ is obtained below:

$x¯=∑xn=23+17+15+30+255=22$

The value of $∑(x−x¯)2$ is obtained below:

x	$x−x¯$	$(x−x¯)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−x¯)2=148$

The sample variance using the defining formula is given below:

$s2=1485−1=1484=37$

Thus, the sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is given below:

$s=1485−1=1484=6.08$

Thus, the sample standard deviation using the defining formula is 6.08.

e.

To determine

Find the population variance using the defining formula.

Find the population standard deviation using the defining formula.

e.

Expert Solution

Answer to Problem 13P

The population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is 5.44.

Explanation of Solution

The population variance using the defining formula is given below:

$σ2=∑(x−μ)2n$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The population standard deviation using the defining formula is given below:

$σ=∑(x−μ)2N$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The value of $μ$ is obtained below:

$μ=∑xN=23+17+15+30+255=22$

The value of $∑(x−μ)2$ is obtained below:

x	$x−μ$	$(x−μ)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−μ)2=148$

The population variance using the defining formula is given below:

$σ2=1485=29.6$

Thus, the population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is given below:

$σ=1485=5.44$

Thus, the population standard deviation using the defining formula is 5.44.

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Answer 5

Chapter 3.2, Problem 13P

a.

To determine

Find the range.

a.

Expert Solution

Answer to Problem 13P

The range is 15.

Explanation of Solution

The range is obtained below:

$Range=Largest value−Smallest value=30−15=15$

Thus, the range is 15.

b.

To determine

Verify that $∑x=110$ and $∑x2=2568$ using calculator.

b.

Expert Solution

Explanation of Solution

Step-by-step procedure to verify $∑x=110$ and $∑x2=2568$ using Ti83 calculator:

Press STAT.
Select Edit.
Enter the values in L1.
Press STAT and Choose CALC.
Select 1-Var Stats.
To select the variable L1, Press 2-nd and then press 1.
Press Enter.

Output obtained using the Ti83 calculator is given below:

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 3.2, Problem 13P

From the output, the values of $∑x=110$ and $∑x2=2,568$ .

c.

To determine

Find the sample variance and the sample standard deviation using the computation formula.

c.

Expert Solution

Answer to Problem 13P

The sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is 6.08.

Explanation of Solution

The sample variance using the computation formula is given below:

$s2=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the computation formula is given below:

$s=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample variance using the computation formula is obtained below:

$s2=2,568−(110)255−1=37$

Thus, the sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is obtained below:

$s=2,568−(110)255−1=37=6.08$

Thus, the sample standard deviation using the computation formula is 6.08.

d.

To determine

Find the sample variance using the defining formula.

Find the sample standard deviation using the defining formula.

d.

Expert Solution

Answer to Problem 13P

The sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is 6.08.

Explanation of Solution

The sample variance using the defining formula is given below:

$s2=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the defining formula is given below:

$s=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The value of $x¯$ is obtained below:

$x¯=∑xn=23+17+15+30+255=22$

The value of $∑(x−x¯)2$ is obtained below:

x	$x−x¯$	$(x−x¯)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−x¯)2=148$

The sample variance using the defining formula is given below:

$s2=1485−1=1484=37$

Thus, the sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is given below:

$s=1485−1=1484=6.08$

Thus, the sample standard deviation using the defining formula is 6.08.

e.

To determine

Find the population variance using the defining formula.

Find the population standard deviation using the defining formula.

e.

Expert Solution

Answer to Problem 13P

The population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is 5.44.

Explanation of Solution

The population variance using the defining formula is given below:

$σ2=∑(x−μ)2n$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The population standard deviation using the defining formula is given below:

$σ=∑(x−μ)2N$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The value of $μ$ is obtained below:

$μ=∑xN=23+17+15+30+255=22$

The value of $∑(x−μ)2$ is obtained below:

x	$x−μ$	$(x−μ)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−μ)2=148$

The population variance using the defining formula is given below:

$σ2=1485=29.6$

Thus, the population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is given below:

$σ=1485=5.44$

Thus, the population standard deviation using the defining formula is 5.44.

Answer 6

Chapter 3.2, Problem 13P

a.

To determine

Find the range.

a.

Expert Solution

Answer to Problem 13P

The range is 15.

Explanation of Solution

The range is obtained below:

$Range=Largest value−Smallest value=30−15=15$

Thus, the range is 15.

Answer 7

Chapter 3.2, Problem 13P

a.

To determine

Find the range.

Answer 8

a.

Expert Solution

Answer to Problem 13P

The range is 15.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The range is obtained below:

$Range=Largest value−Smallest value=30−15=15$

Thus, the range is 15.

Answer 13

b.

To determine

Verify that $∑x=110$ and $∑x2=2568$ using calculator.

b.

Expert Solution

Explanation of Solution

Step-by-step procedure to verify $∑x=110$ and $∑x2=2568$ using Ti83 calculator:

Press STAT.
Select Edit.
Enter the values in L1.
Press STAT and Choose CALC.
Select 1-Var Stats.
To select the variable L1, Press 2-nd and then press 1.
Press Enter.

Output obtained using the Ti83 calculator is given below:

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 3.2, Problem 13P

From the output, the values of $∑x=110$ and $∑x2=2,568$ .

Answer 14

b.

To determine

Verify that $∑x=110$ and $∑x2=2568$ using calculator.

Answer 15

b.

Expert Solution

Explanation of Solution

Step-by-step procedure to verify $∑x=110$ and $∑x2=2568$ using Ti83 calculator:

Press STAT.
Select Edit.
Enter the values in L1.
Press STAT and Choose CALC.
Select 1-Var Stats.
To select the variable L1, Press 2-nd and then press 1.
Press Enter.

Output obtained using the Ti83 calculator is given below:

WebAssign Printed Access Card for Brase/Brase's Understandable Statistics: Concepts and Methods, 12th Edition, Single-Term, Chapter 3.2, Problem 13P

From the output, the values of $∑x=110$ and $∑x2=2,568$ .

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

c.

To determine

Find the sample variance and the sample standard deviation using the computation formula.

c.

Expert Solution

Answer to Problem 13P

The sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is 6.08.

Explanation of Solution

The sample variance using the computation formula is given below:

$s2=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the computation formula is given below:

$s=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample variance using the computation formula is obtained below:

$s2=2,568−(110)255−1=37$

Thus, the sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is obtained below:

$s=2,568−(110)255−1=37=6.08$

Thus, the sample standard deviation using the computation formula is 6.08.

Answer 20

c.

To determine

Find the sample variance and the sample standard deviation using the computation formula.

Answer 21

c.

Expert Solution

Answer to Problem 13P

The sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is 6.08.

Answer 22

c.

Expert Solution

Answer 23

c.

Expert Solution

Answer 24

Expert Solution

Answer 25

Explanation of Solution

The sample variance using the computation formula is given below:

$s2=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the computation formula is given below:

$s=∑x2−(∑x)2nn−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample variance using the computation formula is obtained below:

$s2=2,568−(110)255−1=37$

Thus, the sample variance using the computation formula is 37.

The sample standard deviation using the computation formula is obtained below:

$s=2,568−(110)255−1=37=6.08$

Thus, the sample standard deviation using the computation formula is 6.08.

Answer 26

d.

To determine

Find the sample variance using the defining formula.

Find the sample standard deviation using the defining formula.

d.

Expert Solution

Answer to Problem 13P

The sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is 6.08.

Explanation of Solution

The sample variance using the defining formula is given below:

$s2=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the defining formula is given below:

$s=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The value of $x¯$ is obtained below:

$x¯=∑xn=23+17+15+30+255=22$

The value of $∑(x−x¯)2$ is obtained below:

x	$x−x¯$	$(x−x¯)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−x¯)2=148$

The sample variance using the defining formula is given below:

$s2=1485−1=1484=37$

Thus, the sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is given below:

$s=1485−1=1484=6.08$

Thus, the sample standard deviation using the defining formula is 6.08.

Answer 27

d.

To determine

Find the sample variance using the defining formula.

Find the sample standard deviation using the defining formula.

Answer 28

d.

Expert Solution

Answer to Problem 13P

The sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is 6.08.

Answer 29

d.

Expert Solution

Answer 30

d.

Expert Solution

Answer 31

Expert Solution

Answer 32

Explanation of Solution

The sample variance using the defining formula is given below:

$s2=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The sample standard deviation using the defining formula is given below:

$s=∑(x−x¯)2n−1$

Where $x¯$ is the mean, n is the number of values in the data, and x is the value in the data.

The value of $x¯$ is obtained below:

$x¯=∑xn=23+17+15+30+255=22$

The value of $∑(x−x¯)2$ is obtained below:

x	$x−x¯$	$(x−x¯)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−x¯)2=148$

The sample variance using the defining formula is given below:

$s2=1485−1=1484=37$

Thus, the sample variance using the defining formula is 37.

The sample standard deviation using the defining formula is given below:

$s=1485−1=1484=6.08$

Thus, the sample standard deviation using the defining formula is 6.08.

Answer 33

e.

To determine

Find the population variance using the defining formula.

Find the population standard deviation using the defining formula.

e.

Expert Solution

Answer to Problem 13P

The population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is 5.44.

Explanation of Solution

The population variance using the defining formula is given below:

$σ2=∑(x−μ)2n$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The population standard deviation using the defining formula is given below:

$σ=∑(x−μ)2N$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The value of $μ$ is obtained below:

$μ=∑xN=23+17+15+30+255=22$

The value of $∑(x−μ)2$ is obtained below:

x	$x−μ$	$(x−μ)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−μ)2=148$

The population variance using the defining formula is given below:

$σ2=1485=29.6$

Thus, the population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is given below:

$σ=1485=5.44$

Thus, the population standard deviation using the defining formula is 5.44.

Answer 34

e.

To determine

Find the population variance using the defining formula.

Find the population standard deviation using the defining formula.

Answer 35

e.

Expert Solution

Answer to Problem 13P

The population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is 5.44.

Answer 36

e.

Expert Solution

Answer 37

e.

Expert Solution

Answer 38

Expert Solution

Answer 39

Explanation of Solution

The population variance using the defining formula is given below:

$σ2=∑(x−μ)2n$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The population standard deviation using the defining formula is given below:

$σ=∑(x−μ)2N$

Where $μ$ is the population mean, N is the number of values in the population, and x is the value in the data.

The value of $μ$ is obtained below:

$μ=∑xN=23+17+15+30+255=22$

The value of $∑(x−μ)2$ is obtained below:

x	$x−μ$	$(x−μ)2$
23	1	1
17	–5	25
15	–7	49
30	8	64
25	3	9
		$∑(x−μ)2=148$

The population variance using the defining formula is given below:

$σ2=1485=29.6$

Thus, the population variance using the defining formula is 29.6.

The population standard deviation using the defining formula is given below:

$σ=1485=5.44$

Thus, the population standard deviation using the defining formula is 5.44.

Answer 40

Ch. 3.1 - Statistical Literacy Consider the mode, median,...Ch. 3.1 - Prob. 2P Ch. 3.1 - Prob. 3P Ch. 3.1 - Prob. 4P Ch. 3.1 - Prob. 5P Ch. 3.1 - Basic Computation: Mean, Median, Mode Find the...Ch. 3.1 - Prob. 7P Ch. 3.1 - Critical Thinking Consider a data set with at...Ch. 3.1 - Critical Thinking Consider a data set with at...Ch. 3.1 - Prob. 10P

Find the range .

Videos

Find the range.

Answer to Problem 13P

Explanation of Solution

Verify that $∑x=110$ and $∑x2=2568$ using calculator.

Explanation of Solution

Find the sample variance and the sample standard deviation using the computation formula.

Answer to Problem 13P

Explanation of Solution

Find the sample variance using the defining formula.

Find the sample standard deviation using the defining formula.

Answer to Problem 13P

Explanation of Solution

Find the population variance using the defining formula.

Find the population standard deviation using the defining formula.

Answer to Problem 13P

Explanation of Solution

Want to see more full solutions like this?

Chapter 3 Solutions

Find the range .

Videos

Find the range.

Answer to Problem 13P

Explanation of Solution

Explanation of Solution

Find the sample variance and the sample standard deviation using the computation formula.

Answer to Problem 13P

Explanation of Solution

Find the sample variance using the defining formula. Find the sample standard deviation using the defining formula.

Answer to Problem 13P

Explanation of Solution

Find the population variance using the defining formula. Find the population standard deviation using the defining formula.

Answer to Problem 13P

Explanation of Solution

Want to see more full solutions like this?

Chapter 3 Solutions

Find the sample variance using the defining formula.

Find the sample standard deviation using the defining formula.

Find the population variance using the defining formula.

Find the population standard deviation using the defining formula.