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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 44,36,34,30,23,26,34

 



Answer:_______________




2)  

Calculate the standard deviation.

Natural numbers are 40,39,33,29,20,28,33

 



Answer:_______________




3)  

Calculate the standard deviation.

Natural numbers are 42,38,34,29,22,28,34

 



Answer:_______________




4)  

Calculate the standard deviation.

Natural numbers are 42,39,33,31,20,26,33

 



Answer:_______________




5)  

Calculate the standard deviation.

Natural numbers are 44,39,35,31,21,28,35

 



Answer:_______________




6)  

Calculate the standard deviation.

Natural numbers are 40,38,32,30,24,27,32

 



Answer:_______________




7)  

Calculate the standard deviation.

Natural numbers are 44,37,35,29,21,28,35

 



Answer:_______________




8)  

Calculate the standard deviation.

Natural numbers are 44,36,34,31,24,27,34

 



Answer:_______________




9)  

Calculate the standard deviation.

Natural numbers are 41,38,34,29,25,27,34

 



Answer:_______________




10)  

Calculate the standard deviation.

Natural numbers are 40,36,32,29,24,28,32

 



Answer:_______________




 

1)  

Calculate the standard deviation.

Natural numbers are 44,36,34,30,23,26,34

  Answer: 6.41


SOLUTION 1 :

Assumed Mean Method

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

x

d = x- 34

d2

23

26

30

34

34

36

44

 

 -11

-8

-4

0

0

2

10

 

121

64

16

0

0

4

100

 

  ∑d= -11 ∑d2 = 305

 

 Here, n = 7

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

 

 =     (3057)  -    (-117 )2

=   (43.57 - (-1.57)2)

=   (43.57-2.46)

=   41.11

standard deviation Ô = 6.41

 



2)  

Calculate the standard deviation.

Natural numbers are 40,39,33,29,20,28,33

  Answer: 6.36


SOLUTION 1 :

Assumed Mean Method

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

x

d = x- 33

d2

20

28

29

33

33

39

40

 

 -13

-5

-4

0

0

6

7

 

169

25

16

0

0

36

49

 

  ∑d= -9 ∑d2 = 295

 

 Here, n = 7

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

 

 =     (2957)  -    (-97 )2

=   (42.14 - (-1.29)2)

=   (42.14-1.66)

=   40.48

standard deviation Ô = 6.36

 



3)  

Calculate the standard deviation.

Natural numbers are 42,38,34,29,22,28,34

  Answer: 6.18


SOLUTION 1 :

Assumed Mean Method

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

x

d = x- 34

d2

22

28

29

34

34

38

42

 

 -12

-6

-5

0

0

4

8

 

144

36

25

0

0

16

64

 

  ∑d= -11 ∑d2 = 285

 

 Here, n = 7

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

 

 =     (2857)  -    (-117 )2

=   (40.71 - (-1.57)2)

=   (40.71-2.46)

=   38.25

standard deviation Ô = 6.18

 



4)  

Calculate the standard deviation.

Natural numbers are 42,39,33,31,20,26,33

  Answer: 6.89


SOLUTION 1 :

Assumed Mean Method

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

x

d = x- 33

d2

20

26

31

33

33

39

42

 

 -13

-7

-2

0

0

6

9

 

169

49

4

0

0

36

81

 

  ∑d= -7 ∑d2 = 339

 

 Here, n = 7

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

 

 =     (3397)  -    (-77 )2

=   (48.43 - (-1.00)2)

=   (48.43-1.00)

=   47.43

standard deviation Ô = 6.89

 



5)  

Calculate the standard deviation.

Natural numbers are 44,39,35,31,21,28,35

  Answer: 6.94


SOLUTION 1 :

Assumed Mean Method

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

x

d = x- 35

d2

21

28

31

35

35

39

44

 

 -14

-7

-4

0

0

4

9

 

196

49

16

0

0

16

81

 

  ∑d= -12 ∑d2 = 358

 

 Here, n = 7

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

 

 =     (3587)  -    (-127 )2

=   (51.14 - (-1.71)2)

=   (51.14-2.92)

=   48.22

standard deviation Ô = 6.94

 



6)  

Calculate the standard deviation.

Natural numbers are 40,38,32,30,24,27,32

  Answer: 5.25


SOLUTION 1 :

Assumed Mean Method

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

x

d = x- 32

d2

24

27

30

32

32

38

40

 

 -8

-5

-2

0

0

6

8

 

64

25

4

0

0

36

64

 

  ∑d= -1 ∑d2 = 193

 

 Here, n = 7

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

 

 =     (1937)  -    (-17 )2

=   (27.57 - (-0.14)2)

=   (27.57-0.02)

=   27.55

standard deviation Ô = 5.25

 



7)  

Calculate the standard deviation.

Natural numbers are 44,37,35,29,21,28,35

  Answer: 6.86


SOLUTION 1 :

Assumed Mean Method

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

x

d = x- 35

d2

21

28

29

35

35

37

44

 

 -14

-7

-6

0

0

2

9

 

196

49

36

0

0

4

81

 

  ∑d= -16 ∑d2 = 366

 

 Here, n = 7

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

 

 =     (3667)  -    (-167 )2

=   (52.29 - (-2.29)2)

=   (52.29-5.24)

=   47.05

standard deviation Ô = 6.86

 



8)  

Calculate the standard deviation.

Natural numbers are 44,36,34,31,24,27,34

  Answer: 6.01


SOLUTION 1 :

Assumed Mean Method

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

x

d = x- 34

d2

24

27

31

34

34

36

44

 

 -10

-7

-3

0

0

2

10

 

100

49

9

0

0

4

100

 

  ∑d= -8 ∑d2 = 262

 

 Here, n = 7

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

 

 =     (2627)  -    (-87 )2

=   (37.43 - (-1.14)2)

=   (37.43-1.30)

=   36.13

standard deviation Ô = 6.01

 



9)  

Calculate the standard deviation.

Natural numbers are 41,38,34,29,25,27,34

  Answer: 5.42


SOLUTION 1 :

Assumed Mean Method

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

x

d = x- 34

d2

25

27

29

34

34

38

41

 

 -9

-7

-5

0

0

4

7

 

81

49

25

0

0

16

49

 

  ∑d= -10 ∑d2 = 220

 

 Here, n = 7

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

 

 =     (2207)  -    (-107 )2

=   (31.43 - (-1.43)2)

=   (31.43-2.04)

=   29.39

standard deviation Ô = 5.42

 



10)  

Calculate the standard deviation.

Natural numbers are 40,36,32,29,24,28,32

  Answer: 4.89


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

29

32

32

36

40

 

 -8

-4

-3

0

0

4

8

 

64

16

9

0

0

16

64

 

  ∑d= -3 ∑d2 = 169

 

 Here, n = 7

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

 

 =     (1697)  -    (-37 )2

=   (24.14 - (-0.43)2)

=   (24.14-0.18)

=   23.96

standard deviation Ô = 4.89