Sasi Math (Revised for 1024)

Scroll:statistics >> standard deviation >> saq (4242)

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.

The following table shows the marks obtained by 42 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	8	9	10	11	12	13	14
frequency f	2	4	9	10	7	6	4

Answer:_______________

The following table shows the marks obtained by 47 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	7	8	9	10	11	12	13
frequency f	4	8	8	13	7	3	4

Answer:_______________

The following table shows the marks obtained by 40 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	7	8	9	10	11	12	13
frequency f	2	4	6	15	5	5	3

Answer:_______________

The following table shows the marks obtained by 40 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	9	10	11	12	13	14	15
frequency f	2	6	8	14	5	2	3

Answer:_______________

The following table shows the marks obtained by 39 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	8	9	10	11	12	13	14
frequency f	2	8	7	11	5	3	3

Answer:_______________

The following table shows the marks obtained by 46 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	11	12	13	14	15	16	17
frequency f	4	8	8	13	5	5	3

Answer:_______________

The following table shows the marks obtained by 41 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	8	9	10	11	12	13	14
frequency f	2	5	9	12	6	3	4

Answer:_______________

The following table shows the marks obtained by 37 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	9	10	11	12	13	14	15
frequency f	3	5	5	11	7	2	4

Answer:_______________

The following table shows the marks obtained by 42 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	8	9	10	11	12	13	14
frequency f	4	8	6	12	5	4	3

Answer:_______________

10)

The following table shows the marks obtained by 44 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	8	9	10	11	12	13	14
frequency f	2	5	8	14	7	3	5

Answer:_______________

The following table shows the marks obtained by 42 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	8	9	10	11	12	13	14
frequency f	2	4	9	10	7	6	4

Answer: 1.62

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	2 4 9 10 7 6 4	16 36 90 110 84 78 56	-3 -2 -1 0 1 2 3	-6 -8 -9 0 7 12 12	18 16 9 0 7 24 36
	∑f =42	∑fx=470	∑d=0	∑fd= 8	∑fd²110

Arithmetric mean	xbar	=	∑ fx	=	470	=	11.19
			∑ f		42

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{110}{42}$
		√ ∑f

= √ 2.62

= 1.62

The following table shows the marks obtained by 47 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	7	8	9	10	11	12	13
frequency f	4	8	8	13	7	3	4

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	4 8 8 13 7 3 4	28 64 72 130 77 36 52	-3 -2 -1 0 1 2 3	-12 -16 -8 0 7 6 12	36 32 8 0 7 12 36
	∑f =47	∑fx=459	∑d=0	∑fd= -11	∑fd²131

Arithmetric mean	xbar	=	∑ fx	=	459	=	9.77
			∑ f		47

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{131}{47}$
		√ ∑f

= √ 2.79

= 1.67

The following table shows the marks obtained by 40 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	7	8	9	10	11	12	13
frequency f	2	4	6	15	5	5	3

Answer: 1.52

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	2 4 6 15 5 5 3	14 32 54 150 55 60 39	-3 -2 -1 0 1 2 3	-6 -8 -6 0 5 10 9	18 16 6 0 5 20 27
	∑f =40	∑fx=404	∑d=0	∑fd= 4	∑fd²92

Arithmetric mean	xbar	=	∑ fx	=	404	=	10.10
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{92}{40}$
		√ ∑f

= √ 2.30

= 1.52

The following table shows the marks obtained by 40 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	9	10	11	12	13	14	15
frequency f	2	6	8	14	5	2	3

Answer: 1.50

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	2 6 8 14 5 2 3	18 60 88 168 65 28 45	-3 -2 -1 0 1 2 3	-6 -12 -8 0 5 4 9	18 24 8 0 5 8 27
	∑f =40	∑fx=472	∑d=0	∑fd= -8	∑fd²90

Arithmetric mean	xbar	=	∑ fx	=	472	=	11.80
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{90}{40}$
		√ ∑f

= √ 2.25

= 1.50

The following table shows the marks obtained by 39 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	8	9	10	11	12	13	14
frequency f	2	8	7	11	5	3	3

Answer: 1.61

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	2 8 7 11 5 3 3	16 72 70 121 60 39 42	-3 -2 -1 0 1 2 3	-6 -16 -7 0 5 6 9	18 32 7 0 5 12 27
	∑f =39	∑fx=420	∑d=0	∑fd= -9	∑fd²101

Arithmetric mean	xbar	=	∑ fx	=	420	=	10.77
			∑ f		39

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{101}{39}$
		√ ∑f

= √ 2.59

= 1.61

The following table shows the marks obtained by 46 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	11	12	13	14	15	16	17
frequency f	4	8	8	13	5	5	3

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	4 8 8 13 5 5 3	44 96 104 182 75 80 51	-3 -2 -1 0 1 2 3	-12 -16 -8 0 5 10 9	36 32 8 0 5 20 27
	∑f =46	∑fx=632	∑d=0	∑fd= -12	∑fd²128

Arithmetric mean	xbar	=	∑ fx	=	632	=	13.74
			∑ f		46

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{128}{46}$
		√ ∑f

= √ 2.78

= 1.67

The following table shows the marks obtained by 41 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	8	9	10	11	12	13	14
frequency f	2	5	9	12	6	3	4

Answer: 1.57

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	2 5 9 12 6 3 4	16 45 90 132 72 39 56	-3 -2 -1 0 1 2 3	-6 -10 -9 0 6 6 12	18 20 9 0 6 12 36
	∑f =41	∑fx=450	∑d=0	∑fd= -1	∑fd²101

Arithmetric mean	xbar	=	∑ fx	=	450	=	10.98
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{101}{41}$
		√ ∑f

= √ 2.46

= 1.57

The following table shows the marks obtained by 37 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	9	10	11	12	13	14	15
frequency f	3	5	5	11	7	2	4

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	3 5 5 11 7 2 4	27 50 55 132 91 28 60	-3 -2 -1 0 1 2 3	-9 -10 -5 0 7 4 12	27 20 5 0 7 8 36
	∑f =37	∑fx=443	∑d=0	∑fd= -1	∑fd²103

Arithmetric mean	xbar	=	∑ fx	=	443	=	11.97
			∑ f		37

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{103}{37}$
		√ ∑f

= √ 2.78

= 1.67

The following table shows the marks obtained by 42 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	8	9	10	11	12	13	14
frequency f	4	8	6	12	5	4	3

Answer: 1.70

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	4 8 6 12 5 4 3	32 72 60 132 60 52 42	-3 -2 -1 0 1 2 3	-12 -16 -6 0 5 8 9	36 32 6 0 5 16 27
	∑f =42	∑fx=450	∑d=0	∑fd= -12	∑fd²122

Arithmetric mean	xbar	=	∑ fx	=	450	=	10.71
			∑ f		42

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{122}{42}$
		√ ∑f

= √ 2.90

= 1.70

10)

The following table shows the marks obtained by 44 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	8	9	10	11	12	13	14
frequency f	2	5	8	14	7	3	5

Answer: 1.58

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	2 5 8 14 7 3 5	16 45 80 154 84 39 70	-3 -2 -1 0 1 2 3	-6 -10 -8 0 7 6 15	18 20 8 0 7 12 45
	∑f =44	∑fx=488	∑d=0	∑fd= 4	∑fd²110

Arithmetric mean	xbar	=	∑ fx	=	488	=	11.09
			∑ f		44

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{110}{44}$
		√ ∑f

= √ 2.50

= 1.58