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Calculate the range, variance, and standard deviation for the following samples:

a.4, 2, 1, 0, 1

b.1, 6, 2, 2, 3, 0, 3

c.8, -2, 1, 3, 5, 4, 4, 1, 3, 3

d.0, 2, 0, 0, -1, 1, -2, 1, 0, -1, 1, -1, 0, -3,-2, -1, 0, 1

Short Answer

Expert verified
  1. Range = 4, Variance = 2.3, Standard Deviation = 1.52
  2. Range = 6, Variance = 3.619, Standard Deviation = 1.90
  3. Range = 10, Variance = 7.11, Standard Deviation = 2.66
  4. Range = 5, Variance = 0.4966, Standard Deviation = 0.70

Step by step solution

01

Step-by-Step SolutionsStep 1: Calculating the range, variance, and standard deviation of a4, 2, 1, 0, 1

Range = 4 鈥 0 = 4

Mean(-)=N=4+2+1+0+15=85=1.6=1.6

Mean(-)=N=4+2+1+0+15=85=1.6

-=1.6

Variance=(蠂-)2N1=9.251=9.24=2.3

Therefore, the variance is 2.3

Standarddeviation=Variance=2.3=1.52

Therefore, the standard deviation is 1.52.

02

Finding the range, variance, and standard deviation of b1, 6, 2, 2, 3, 0, 3

Range = 6 鈥 0 = 6

X

(XX)

(XX)2

1

1 鈥 2.43 = -1.43

2.0449

6

6 鈥 2.43 = 3.57

12.7449

2

2 鈥 2.43 = -0.43

0.1849

2

2 鈥 2.43 = -0.43

0.1849

3

3 鈥 2.43 = 0.57

0.3249

0

0 鈥 2.43 = -2.43

5.9049

3

3 鈥 2.43 = 0.57

0.3249

Sum

0

21.7143

localid="1651305337400" Mean(-)=N=1+6+2+2+3+0+37=177=2.43

localid="1651305447844" -=2.43

localid="1651305675002" Variance=(蠂-)2N1=21.714371=21.71436=3.619

Therefore, the variance is 3.619.

Standarddeviation=Variance=3.619=1.90

Therefore, the standard deviation is 1.90.

03

Estimating the range, variance, and standard deviation of c8, -2, 1, 3, 5, 4, 4, 1, 3, 3

Range = 8 鈥 (-2) = 10

Mean(-)=N=8+(2)+1+3+5+4+4+1+3+310=3010=3

-=3

Variance=(蠂-)2N1=64101=649=7.11

Therefore, the variance is 7.11.

Standarddeviation=Variance=7.11=2.66

Therefore, the standard deviation is 2.66.

04

Computing the range, variance, and standard deviation of d0, 2, 0, 0, -1, 1, -2, 1, 0, -1, 1, -1, 0, -3,-2, -1, 0, 1

Range = 2 鈥 (-3) = 5

X

(XX)

(XX)2

0

0 鈥 (-0.27) = 0.27

0.0729

2

2 鈥 (-0.27) = 2.27

5.1529

0

0 鈥 (-0.27) = 0.27

0.0729

0

0 鈥 (-0.27) = 0.27

0.0729

-1

(-1) 鈥 (-0.27) = -0.73

-0.5329

1

1 鈥 (-0.27) = 1.27

1.6129

-2

(-2) 鈥 (-0.27) = -1.73

2.9929

1

1 鈥 (-0.27) = 1.27

1.6129

0

0 鈥 (-0.27) = 0.27

0.0729

-1

(-1) 鈥 (-0.27) = -0.73

-0.5329

1

1 鈥 (-0.27) = 1.27

1.6129

-1

(-1) 鈥 (-0.27) = -0.73

-0.5329

0

0 鈥 (-0.27) = 0.27

0.0729

-3

(-3) - (-0.27) = -2.73

-7.4529

-2

(-2) 鈥 (-0.27) = -1.73

2.9929

-1

(-1) 鈥 (-0.27) = -0.73

-0.5329

0

0 鈥 (-0.27) = 0.27

0.0729

1

1 鈥 (-0.27) = 1.27

1.6129

Sum

0

8.4432

Mean(-)=N=0+2+0+0+(1)+1+(2)+1+0+(1)+1+(1)+0+(3)+(2)+(1)+0+118=518=0.27

-=0.27

Variance=(蠂-)2N1=8.4432181=8.443217=0.4966

Therefore, the variance is 0.4966.

Standarddeviation=Variance=0.4966=0.70

Therefore, the standard deviation is 0.70.

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