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Chapter 2: Q60E (page 103)

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

a.39, 42, 40, 37, 41

b.100, 4, 7, 96, 80, 3, 1, 10, 2

c.100, 4, 7, 30, 80, 30, 42, 2

Short Answer

Expert verified
  1. Range = 5, Variance = 3.79, Standard Deviation = 1.95
  2. Range = 99, Variance = 1949.25, Standard Deviation = 44.15
  3. Range = 98, Variance = 1307.839, Standard Deviation = 36.16

Step by step solution

01

Calculating the range, variance and standard deviation for a

39, 42, 40, 37, 41

Range = 42 – 37 = 5

x

2

39

-0.8

0.64

42

2.2

4.84

40

0.2

0.4

37

-2.8

7.84

41

1.2

1.44

Sum

0

15.16

Mean(x¯)=sumofxn=1995=39.8

Variance=∑(x-x¯)2n-1=15.165-1=15.164=3.79

StandardDeviation=Variance=3.79=1.95

Therefore,the variance and standard deviation are 3.79 and 1.95 respectively.

02

Finding the range, variance and standard deviation for b

100, 4, 7, 96, 80, 3, 1, 10, 2

Range = 100 – 1 = 99

x

2

100

66.33

4400.11

4

-29.67

880.11

7

-26.67

711.11

96

62.33

3885.44

80

46.33

2146.778

3

-30.67

940.44

1

-32.67

1067.11

10

-23.67

560.11

2

-31.67

1002.778

Sum

0

15594

Mean(x¯)=sumofxn=3019=33.66

Variance=∑(x-x¯)2n-1=155949-1=155948=1949.25

StandardDeviation=Variance=1949.25=44.15

Therefore, Variance = 1949.25 and Standard Deviation = 44.15

03

Computing the range, variance and standard deviation for c

100, 4, 7, 30, 80, 30, 42, 2

Range = 100 – 2 = 98

x

2

100

63.125

3984.766

4

-32.875

1080.766

7

-29.875

892.5156

30

-6.875

47.26563

80

43.125

1859.766

30

-6.875

47.26563

42

5.125

26.26563

2

-34.875

1216.266

Sum

0

9154.875

Mean(x¯)=sumofxn=2958=36.875

Variance=∑(x-x¯)2n-1=9154.8758-1=9154.8757=1307.839

StandardDeviation=Variance=1307.839=36.16

Hence, thevariance is 1307.839 and standard deviation is 36.16.

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