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 48 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer:_______________

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

data x	10	11	12	13	14	15	16
frequency f	3	5	6	10	7	6	3

Answer:_______________

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

data x	11	12	13	14	15	16	17
frequency f	3	4	9	14	7	4	3

Answer:_______________

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

data x	9	10	11	12	13	14	15
frequency f	4	4	7	11	6	3	4

Answer:_______________

The following table shows the marks obtained by 43 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer:_______________

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

data x	11	12	13	14	15	16	17
frequency f	2	6	9	13	6	2	3

Answer:_______________

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

data x	11	12	13	14	15	16	17
frequency f	2	5	6	13	7	4	5

Answer:_______________

The following table shows the marks obtained by 43 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer:_______________

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

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

Answer:_______________

10)

The following table shows the marks obtained by 45 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	9	10	11	12	13	14	15
frequency f	3	7	8	11	6	5	5

Answer:_______________

The following table shows the marks obtained by 48 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.56

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	2 6 8 15 7 6 4	14 48 72 150 77 72 52	-3 -2 -1 0 1 2 3	-6 -12 -8 0 7 12 12	18 24 8 0 7 24 36
	∑f =48	∑fx=485	∑d=0	∑fd= 5	∑fd²117

Arithmetric mean	xbar	=	∑ fx	=	485	=	10.10
			∑ f		48

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{117}{48}$
		√ ∑f

= √ 2.44

= 1.56

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

data x	10	11	12	13	14	15	16
frequency f	3	5	6	10	7	6	3

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	3 5 6 10 7 6 3	30 55 72 130 98 90 48	-3 -2 -1 0 1 2 3	-9 -10 -6 0 7 12 9	27 20 6 0 7 24 27
	∑f =40	∑fx=523	∑d=0	∑fd= 3	∑fd²111

Arithmetric mean	xbar	=	∑ fx	=	523	=	13.08
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{111}{40}$
		√ ∑f

= √ 2.78

= 1.67

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

data x	11	12	13	14	15	16	17
frequency f	3	4	9	14	7	4	3

Answer: 1.52

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	3 4 9 14 7 4 3	33 48 117 196 105 64 51	-3 -2 -1 0 1 2 3	-9 -8 -9 0 7 8 9	27 16 9 0 7 16 27
	∑f =44	∑fx=614	∑d=0	∑fd= -2	∑fd²102

Arithmetric mean	xbar	=	∑ fx	=	614	=	13.95
			∑ f		44

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{102}{44}$
		√ ∑f

= √ 2.32

= 1.52

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

data x	9	10	11	12	13	14	15
frequency f	4	4	7	11	6	3	4

Answer: 1.70

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	4 4 7 11 6 3 4	36 40 77 132 78 42 60	-3 -2 -1 0 1 2 3	-12 -8 -7 0 6 6 12	36 16 7 0 6 12 36
	∑f =39	∑fx=465	∑d=0	∑fd= -3	∑fd²113

Arithmetric mean	xbar	=	∑ fx	=	465	=	11.92
			∑ f		39

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{113}{39}$
		√ ∑f

= √ 2.90

= 1.70

The following table shows the marks obtained by 43 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.52

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	2 7 7 14 7 3 3	14 56 63 140 77 36 39	-3 -2 -1 0 1 2 3	-6 -14 -7 0 7 6 9	18 28 7 0 7 12 27
	∑f =43	∑fx=425	∑d=0	∑fd= -5	∑fd²99

Arithmetric mean	xbar	=	∑ fx	=	425	=	9.88
			∑ f		43

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{99}{43}$
		√ ∑f

= √ 2.30

= 1.52

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

data x	11	12	13	14	15	16	17
frequency f	2	6	9	13	6	2	3

Answer: 1.50

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	2 6 9 13 6 2 3	22 72 117 182 90 32 51	-3 -2 -1 0 1 2 3	-6 -12 -9 0 6 4 9	18 24 9 0 6 8 27
	∑f =41	∑fx=566	∑d=0	∑fd= -8	∑fd²92

Arithmetric mean	xbar	=	∑ fx	=	566	=	13.80
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{92}{41}$
		√ ∑f

= √ 2.24

= 1.50

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

data x	11	12	13	14	15	16	17
frequency f	2	5	6	13	7	4	5

Answer: 1.63

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	2 5 6 13 7 4 5	22 60 78 182 105 64 85	-3 -2 -1 0 1 2 3	-6 -10 -6 0 7 8 15	18 20 6 0 7 16 45
	∑f =42	∑fx=596	∑d=0	∑fd= 8	∑fd²112

Arithmetric mean	xbar	=	∑ fx	=	596	=	14.19
			∑ f		42

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{112}{42}$
		√ ∑f

= √ 2.67

= 1.63

The following table shows the marks obtained by 43 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.74

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 7 7 10 7 4 5	21 56 63 100 77 48 65	-3 -2 -1 0 1 2 3	-9 -14 -7 0 7 8 15	27 28 7 0 7 16 45
	∑f =43	∑fx=430	∑d=0	∑fd= 0	∑fd²130

Arithmetric mean	xbar	=	∑ fx	=	430	=	10.00
			∑ f		43

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{130}{43}$
		√ ∑f

= √ 3.02

= 1.74

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

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

Answer: 1.79

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	4 7 9 10 5 6 5	28 56 81 100 55 72 65	-3 -2 -1 0 1 2 3	-12 -14 -9 0 5 12 15	36 28 9 0 5 24 45
	∑f =46	∑fx=457	∑d=0	∑fd= -3	∑fd²147

Arithmetric mean	xbar	=	∑ fx	=	457	=	9.93
			∑ f		46

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{147}{46}$
		√ ∑f

= √ 3.20

= 1.79

10)

The following table shows the marks obtained by 45 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	9	10	11	12	13	14	15
frequency f	3	7	8	11	6	5	5

Answer: 1.73

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	3 7 8 11 6 5 5	27 70 88 132 78 70 75	-3 -2 -1 0 1 2 3	-9 -14 -8 0 6 10 15	27 28 8 0 6 20 45
	∑f =45	∑fx=540	∑d=0	∑fd= 0	∑fd²134

Arithmetric mean	xbar	=	∑ fx	=	540	=	12.00
			∑ f		45

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{134}{45}$
		√ ∑f

= √ 2.98

= 1.73