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

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

Answer:_______________

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

data x	10	11	12	13	14	15	16
frequency f	4	8	8	11	5	3	5

Answer:_______________

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

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

Answer:_______________

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

data x	8	9	10	11	12	13	14
frequency f	2	6	9	12	7	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	10	11	12	13	14	15	16
frequency f	2	4	6	12	7	3	3

Answer:_______________

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

data x	9	10	11	12	13	14	15
frequency f	4	4	6	15	6	5	4

Answer:_______________

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

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

Answer:_______________

10)

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

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

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	3	6	6	13	6	3	4

Answer: 1.65

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	3 6 6 13 6 3 4	24 54 60 143 72 39 56	-3 -2 -1 0 1 2 3	-9 -12 -6 0 6 6 12	27 24 6 0 6 12 36
	∑f =41	∑fx=448	∑d=0	∑fd= -3	∑fd²111

Arithmetric mean	xbar	=	∑ fx	=	448	=	10.93
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{111}{41}$
		√ ∑f

= √ 2.71

= 1.65

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	3	5	7	10	6	5	4

Answer: 1.70

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	3 5 7 10 6 5 4	27 50 77 120 78 70 60	-3 -2 -1 0 1 2 3	-9 -10 -7 0 6 10 12	27 20 7 0 6 20 36
	∑f =40	∑fx=482	∑d=0	∑fd= 2	∑fd²116

Arithmetric mean	xbar	=	∑ fx	=	482	=	12.05
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{116}{40}$
		√ ∑f

= √ 2.90

= 1.70

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	3	6	5	12	6	3	5

Answer: 1.73

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 6 5 12 6 3 5	21 48 45 120 66 36 65	-3 -2 -1 0 1 2 3	-9 -12 -5 0 6 6 15	27 24 5 0 6 12 45
	∑f =40	∑fx=401	∑d=0	∑fd= 1	∑fd²119

Arithmetric mean	xbar	=	∑ fx	=	401	=	10.03
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{119}{40}$
		√ ∑f

= √ 2.98

= 1.73

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

data x	10	11	12	13	14	15	16
frequency f	4	8	8	11	5	3	5

Answer: 1.77

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	4 8 8 11 5 3 5	40 88 96 143 70 45 80	-3 -2 -1 0 1 2 3	-12 -16 -8 0 5 6 15	36 32 8 0 5 12 45
	∑f =44	∑fx=562	∑d=0	∑fd= -10	∑fd²138

Arithmetric mean	xbar	=	∑ fx	=	562	=	12.77
			∑ f		44

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{138}{44}$
		√ ∑f

= √ 3.14

= 1.77

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

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

Answer: 1.75

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	3 6 5 10 5 4 4	24 54 50 110 60 52 56	-3 -2 -1 0 1 2 3	-9 -12 -5 0 5 8 12	27 24 5 0 5 16 36
	∑f =37	∑fx=406	∑d=0	∑fd= -1	∑fd²113

Arithmetric mean	xbar	=	∑ fx	=	406	=	10.97
			∑ f		37

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{113}{37}$
		√ ∑f

= √ 3.05

= 1.75

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

data x	8	9	10	11	12	13	14
frequency f	2	6	9	12	7	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 6 9 12 7 3 4	16 54 90 132 84 39 56	-3 -2 -1 0 1 2 3	-6 -12 -9 0 7 6 12	18 24 9 0 7 12 36
	∑f =43	∑fx=471	∑d=0	∑fd= -2	∑fd²106

Arithmetric mean	xbar	=	∑ fx	=	471	=	10.95
			∑ f		43

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{106}{43}$
		√ ∑f

= √ 2.47

= 1.57

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

data x	10	11	12	13	14	15	16
frequency f	2	4	6	12	7	3	3

Answer: 1.52

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	2 4 6 12 7 3 3	20 44 72 156 98 45 48	-3 -2 -1 0 1 2 3	-6 -8 -6 0 7 6 9	18 16 6 0 7 12 27
	∑f =37	∑fx=483	∑d=0	∑fd= 2	∑fd²86

Arithmetric mean	xbar	=	∑ fx	=	483	=	13.05
			∑ f		37

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{86}{37}$
		√ ∑f

= √ 2.32

= 1.52

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

data x	9	10	11	12	13	14	15
frequency f	4	4	6	15	6	5	4

Answer: 1.65

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	4 4 6 15 6 5 4	36 40 66 180 78 70 60	-3 -2 -1 0 1 2 3	-12 -8 -6 0 6 10 12	36 16 6 0 6 20 36
	∑f =44	∑fx=530	∑d=0	∑fd= 2	∑fd²120

Arithmetric mean	xbar	=	∑ fx	=	530	=	12.05
			∑ f		44

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{120}{44}$
		√ ∑f

= √ 2.73

= 1.65

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

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

Answer: 1.60

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	3 7 6 14 7 5 3	30 77 72 182 98 75 48	-3 -2 -1 0 1 2 3	-9 -14 -6 0 7 10 9	27 28 6 0 7 20 27
	∑f =45	∑fx=582	∑d=0	∑fd= -3	∑fd²115

Arithmetric mean	xbar	=	∑ fx	=	582	=	12.93
			∑ f		45

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{115}{45}$
		√ ∑f

= √ 2.56

= 1.60

10)

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

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

Answer: 1.58

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	2 4 9 12 7 2 5	14 32 81 120 77 24 65	-3 -2 -1 0 1 2 3	-6 -8 -9 0 7 4 15	18 16 9 0 7 8 45
	∑f =41	∑fx=413	∑d=0	∑fd= 3	∑fd²103

Arithmetric mean	xbar	=	∑ fx	=	413	=	10.07
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{103}{41}$
		√ ∑f

= √ 2.51

= 1.58