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	11	12	13	14	15	16	17
frequency f	4	7	8	15	5	6	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	3	8	8	12	7	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	8	9	10	11	12	13	14
frequency f	3	7	6	10	5	6	3

Answer:_______________

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

data x	11	12	13	14	15	16	17
frequency f	3	5	7	15	7	6	5

Answer:_______________

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

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

Answer:_______________

The following table shows the marks obtained by 38 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	10	5	3	4

Answer:_______________

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

data x	11	12	13	14	15	16	17
frequency f	3	7	7	11	7	5	5

Answer:_______________

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

data x	7	8	9	10	11	12	13
frequency f	3	6	7	15	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	8	9	10	11	12	13	14
frequency f	3	4	8	14	6	4	5

Answer:_______________

10)

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	3	7	6	12	7	4	5

Answer:_______________

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

data x	11	12	13	14	15	16	17
frequency f	4	7	8	15	5	6	3

Answer: 1.63

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	4 7 8 15 5 6 3	44 84 104 210 75 96 51	-3 -2 -1 0 1 2 3	-12 -14 -8 0 5 12 9	36 28 8 0 5 24 27
	∑f =48	∑fx=664	∑d=0	∑fd= -8	∑fd²128

Arithmetric mean	xbar	=	∑ fx	=	664	=	13.83
			∑ f		48

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{128}{48}$
		√ ∑f

= √ 2.67

= 1.63

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	3	8	8	12	7	5	3

Answer: 1.62

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	3 8 8 12 7 5 3	33 96 104 168 105 80 51	-3 -2 -1 0 1 2 3	-9 -16 -8 0 7 10 9	27 32 8 0 7 20 27
	∑f =46	∑fx=637	∑d=0	∑fd= -7	∑fd²121

Arithmetric mean	xbar	=	∑ fx	=	637	=	13.85
			∑ f		46

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{121}{46}$
		√ ∑f

= √ 2.63

= 1.62

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

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

Answer: 1.71

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	3 7 6 10 5 6 3	24 63 60 110 60 78 42	-3 -2 -1 0 1 2 3	-9 -14 -6 0 5 12 9	27 28 6 0 5 24 27
	∑f =40	∑fx=437	∑d=0	∑fd= -3	∑fd²117

Arithmetric mean	xbar	=	∑ fx	=	437	=	10.93
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{117}{40}$
		√ ∑f

= √ 2.93

= 1.71

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

data x	11	12	13	14	15	16	17
frequency f	3	5	7	15	7	6	5

Answer: 1.65

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	3 5 7 15 7 6 5	33 60 91 210 105 96 85	-3 -2 -1 0 1 2 3	-9 -10 -7 0 7 12 15	27 20 7 0 7 24 45
	∑f =48	∑fx=680	∑d=0	∑fd= 8	∑fd²130

Arithmetric mean	xbar	=	∑ fx	=	680	=	14.17
			∑ f		48

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{130}{48}$
		√ ∑f

= √ 2.71

= 1.65

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

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

Answer: 1.81

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	4 6 5 10 7 5 5	28 48 45 100 77 60 65	-3 -2 -1 0 1 2 3	-12 -12 -5 0 7 10 15	36 24 5 0 7 20 45
	∑f =42	∑fx=423	∑d=0	∑fd= 3	∑fd²137

Arithmetric mean	xbar	=	∑ fx	=	423	=	10.07
			∑ f		42

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{137}{42}$
		√ ∑f

= √ 3.26

= 1.81

The following table shows the marks obtained by 38 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	10	5	3	4

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	2 7 7 10 5 3 4	14 56 63 100 55 36 52	-3 -2 -1 0 1 2 3	-6 -14 -7 0 5 6 12	18 28 7 0 5 12 36
	∑f =38	∑fx=376	∑d=0	∑fd= -4	∑fd²106

Arithmetric mean	xbar	=	∑ fx	=	376	=	9.89
			∑ f		38

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{106}{38}$
		√ ∑f

= √ 2.79

= 1.67

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

data x	11	12	13	14	15	16	17
frequency f	3	7	7	11	7	5	5

Answer: 1.73

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	3 7 7 11 7 5 5	33 84 91 154 105 80 85	-3 -2 -1 0 1 2 3	-9 -14 -7 0 7 10 15	27 28 7 0 7 20 45
	∑f =45	∑fx=632	∑d=0	∑fd= 2	∑fd²134

Arithmetric mean	xbar	=	∑ fx	=	632	=	14.04
			∑ f		45

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{134}{45}$
		√ ∑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	7	8	9	10	11	12	13
frequency f	3	6	7	15	7	3	3

Answer: 1.54

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 6 7 15 7 3 3	21 48 63 150 77 36 39	-3 -2 -1 0 1 2 3	-9 -12 -7 0 7 6 9	27 24 7 0 7 12 27
	∑f =44	∑fx=434	∑d=0	∑fd= -6	∑fd²104

Arithmetric mean	xbar	=	∑ fx	=	434	=	9.86
			∑ f		44

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{104}{44}$
		√ ∑f

= √ 2.36

= 1.54

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	3	4	8	14	6	4	5

Answer: 1.64

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	3 4 8 14 6 4 5	24 36 80 154 72 52 70	-3 -2 -1 0 1 2 3	-9 -8 -8 0 6 8 15	27 16 8 0 6 16 45
	∑f =44	∑fx=488	∑d=0	∑fd= 4	∑fd²118

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

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{118}{44}$
		√ ∑f

= √ 2.68

= 1.64

10)

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	3	7	6	12	7	4	5

Answer: 1.71

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	3 7 6 12 7 4 5	30 77 72 156 98 60 80	-3 -2 -1 0 1 2 3	-9 -14 -6 0 7 8 15	27 28 6 0 7 16 45
	∑f =44	∑fx=573	∑d=0	∑fd= 1	∑fd²129

Arithmetric mean	xbar	=	∑ fx	=	573	=	13.02
			∑ f		44

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{129}{44}$
		√ ∑f

= √ 2.93

= 1.71