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Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.



 

1)  

Calculate the standard deviation.

Natural numbers are 44,36,34,29,20,26,34

 



Answer:_______________




2)  

Calculate the standard deviation.

Natural numbers are 44,39,34,31,21,26,34

 



Answer:_______________




3)  

Calculate the standard deviation.

Natural numbers are 42,36,34,29,25,28,34

 



Answer:_______________




4)  

Calculate the standard deviation.

Natural numbers are 42,38,35,31,20,26,35

 



Answer:_______________




5)  

Calculate the standard deviation.

Natural numbers are 42,38,34,30,20,28,34

 



Answer:_______________




6)  

Calculate the standard deviation.

Natural numbers are 41,38,33,30,23,27,33

 



Answer:_______________




7)  

Calculate the standard deviation.

Natural numbers are 41,38,34,30,25,28,34

 



Answer:_______________




8)  

Calculate the standard deviation.

Natural numbers are 42,38,35,31,20,27,35

 



Answer:_______________




9)  

Calculate the standard deviation.

Natural numbers are 40,39,32,31,24,28,32

 



Answer:_______________




10)  

Calculate the standard deviation.

Natural numbers are 42,39,34,31,21,27,34

 



Answer:_______________




 

1)  

Calculate the standard deviation.

Natural numbers are 44,36,34,29,20,26,34

  Answer: 7.14


SOLUTION 1 :

Assumed Mean Method

Let us take A = 34 as assumed mean and form the following table.

x

d = x- 34

d2

20

26

29

34

34

36

44

 

 -14

-8

-5

0

0

2

10

 

196

64

25

0

0

4

100

 

  ∑d= -15 ∑d2 = 389

 

 Here, n = 7

standard deviation Ô=  ∑d2 
-
 
  (∑d)2
  n  n2

 

 =     (3897)  -    (-157 )2

=   (55.57 - (-2.14)2)

=   (55.57-4.58)

=   50.99

standard deviation Ô = 7.14

 



2)  

Calculate the standard deviation.

Natural numbers are 44,39,34,31,21,26,34

  Answer: 7.13


SOLUTION 1 :

Assumed Mean Method

Let us take A = 34 as assumed mean and form the following table.

x

d = x- 34

d2

21

26

31

34

34

39

44

 

 -13

-8

-3

0

0

5

10

 

169

64

9

0

0

25

100

 

  ∑d= -9 ∑d2 = 367

 

 Here, n = 7

standard deviation Ô=  ∑d2 
-
 
  (∑d)2
  n  n2

 

 =     (3677)  -    (-97 )2

=   (52.43 - (-1.29)2)

=   (52.43-1.66)

=   50.77

standard deviation Ô = 7.13

 



3)  

Calculate the standard deviation.

Natural numbers are 42,36,34,29,25,28,34

  Answer: 5.29


SOLUTION 1 :

Assumed Mean Method

Let us take A = 34 as assumed mean and form the following table.

x

d = x- 34

d2

25

28

29

34

34

36

42

 

 -9

-6

-5

0

0

2

8

 

81

36

25

0

0

4

64

 

  ∑d= -10 ∑d2 = 210

 

 Here, n = 7

standard deviation Ô=  ∑d2 
-
 
  (∑d)2
  n  n2

 

 =     (2107)  -    (-107 )2

=   (30.00 - (-1.43)2)

=   (30.00-2.04)

=   27.96

standard deviation Ô = 5.29

 



4)  

Calculate the standard deviation.

Natural numbers are 42,38,35,31,20,26,35

  Answer: 6.91


SOLUTION 1 :

Assumed Mean Method

Let us take A = 35 as assumed mean and form the following table.

x

d = x- 35

d2

20

26

31

35

35

38

42

 

 -15

-9

-4

0

0

3

7

 

225

81

16

0

0

9

49

 

  ∑d= -18 ∑d2 = 380

 

 Here, n = 7

standard deviation Ô=  ∑d2 
-
 
  (∑d)2
  n  n2

 

 =     (3807)  -    (-187 )2

=   (54.29 - (-2.57)2)

=   (54.29-6.60)

=   47.69

standard deviation Ô = 6.91

 



5)  

Calculate the standard deviation.

Natural numbers are 42,38,34,30,20,28,34

  Answer: 6.63


SOLUTION 1 :

Assumed Mean Method

Let us take A = 34 as assumed mean and form the following table.

x

d = x- 34

d2

20

28

30

34

34

38

42

 

 -14

-6

-4

0

0

4

8

 

196

36

16

0

0

16

64

 

  ∑d= -12 ∑d2 = 328

 

 Here, n = 7

standard deviation Ô=  ∑d2 
-
 
  (∑d)2
  n  n2

 

 =     (3287)  -    (-127 )2

=   (46.86 - (-1.71)2)

=   (46.86-2.92)

=   43.94

standard deviation Ô = 6.63

 



6)  

Calculate the standard deviation.

Natural numbers are 41,38,33,30,23,27,33

  Answer: 5.72


SOLUTION 1 :

Assumed Mean Method

Let us take A = 33 as assumed mean and form the following table.

x

d = x- 33

d2

23

27

30

33

33

38

41

 

 -10

-6

-3

0

0

5

8

 

100

36

9

0

0

25

64

 

  ∑d= -6 ∑d2 = 234

 

 Here, n = 7

standard deviation Ô=  ∑d2 
-
 
  (∑d)2
  n  n2

 

 =     (2347)  -    (-67 )2

=   (33.43 - (-0.86)2)

=   (33.43-0.74)

=   32.69

standard deviation Ô = 5.72

 



7)  

Calculate the standard deviation.

Natural numbers are 41,38,34,30,25,28,34

  Answer: 5.20


SOLUTION 1 :

Assumed Mean Method

Let us take A = 34 as assumed mean and form the following table.

x

d = x- 34

d2

25

28

30

34

34

38

41

 

 -9

-6

-4

0

0

4

7

 

81

36

16

0

0

16

49

 

  ∑d= -8 ∑d2 = 198

 

 Here, n = 7

standard deviation Ô=  ∑d2 
-
 
  (∑d)2
  n  n2

 

 =     (1987)  -    (-87 )2

=   (28.29 - (-1.14)2)

=   (28.29-1.30)

=   26.99

standard deviation Ô = 5.20

 



8)  

Calculate the standard deviation.

Natural numbers are 42,38,35,31,20,27,35

  Answer: 6.78


SOLUTION 1 :

Assumed Mean Method

Let us take A = 35 as assumed mean and form the following table.

x

d = x- 35

d2

20

27

31

35

35

38

42

 

 -15

-8

-4

0

0

3

7

 

225

64

16

0

0

9

49

 

  ∑d= -17 ∑d2 = 363

 

 Here, n = 7

standard deviation Ô=  ∑d2 
-
 
  (∑d)2
  n  n2

 

 =     (3637)  -    (-177 )2

=   (51.86 - (-2.43)2)

=   (51.86-5.90)

=   45.96

standard deviation Ô = 6.78

 



9)  

Calculate the standard deviation.

Natural numbers are 40,39,32,31,24,28,32

  Answer: 5.26


SOLUTION 1 :

Assumed Mean Method

Let us take A = 32 as assumed mean and form the following table.

x

d = x- 32

d2

24

28

31

32

32

39

40

 

 -8

-4

-1

0

0

7

8

 

64

16

1

0

0

49

64

 

  ∑d= 2 ∑d2 = 194

 

 Here, n = 7

standard deviation Ô=  ∑d2 
-
 
  (∑d)2
  n  n2

 

 =     (1947)  -    (27 )2

=   (27.71 - (0.29)2)

=   (27.71-0.08)

=   27.63

standard deviation Ô = 5.26

 



10)  

Calculate the standard deviation.

Natural numbers are 42,39,34,31,21,27,34

  Answer: 6.57


SOLUTION 1 :

Assumed Mean Method

Let us take A = 34 as assumed mean and form the following table.

x

d = x- 34

d2

21

27

31

34

34

39

42

 

 -13

-7

-3

0

0

5

8

 

169

49

9

0

0

25

64

 

  ∑d= -10 ∑d2 = 316

 

 Here, n = 7

standard deviation Ô=  ∑d2 
-
 
  (∑d)2
  n  n2

 

 =     (3167)  -    (-107 )2

=   (45.14 - (-1.43)2)

=   (45.14-2.04)

=   43.10

standard deviation Ô = 6.57