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

Answer:_______________

The following table shows the marks obtained by 38 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer:_______________

The following table shows the marks obtained by 36 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	11	12	13	14	15	16	17
frequency f	3	6	5	12	5	2	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	4	4	6	11	6	5	5

Answer:_______________

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

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

Answer:_______________

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

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

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

Answer:_______________

10)

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

data x	10	11	12	13	14	15	16
frequency f	2	7	6	12	7	4	5

Answer:_______________

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

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

Answer: 1.74

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	3 4 7 11 5 6 5	27 40 77 132 65 84 75	-3 -2 -1 0 1 2 3	-9 -8 -7 0 5 12 15	27 16 7 0 5 24 45
	∑f =41	∑fx=500	∑d=0	∑fd= 8	∑fd²124

Arithmetric mean	xbar	=	∑ fx	=	500	=	12.20
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{124}{41}$
		√ ∑f

= √ 3.02

= 1.74

The following table shows the marks obtained by 38 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.69

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	2 6 5 11 5 5 4	22 72 65 154 75 80 68	-3 -2 -1 0 1 2 3	-6 -12 -5 0 5 10 12	18 24 5 0 5 20 36
	∑f =38	∑fx=536	∑d=0	∑fd= 4	∑fd²108

Arithmetric mean	xbar	=	∑ fx	=	536	=	14.11
			∑ f		38

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{108}{38}$
		√ ∑f

= √ 2.84

= 1.69

The following table shows the marks obtained by 36 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

data x	11	12	13	14	15	16	17
frequency f	3	6	5	12	5	2	3

Answer: 1.63

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	3 6 5 12 5 2 3	33 72 65 168 75 32 51	-3 -2 -1 0 1 2 3	-9 -12 -5 0 5 4 9	27 24 5 0 5 8 27
	∑f =36	∑fx=496	∑d=0	∑fd= -8	∑fd²96

Arithmetric mean	xbar	=	∑ fx	=	496	=	13.78
			∑ f		36

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{96}{36}$
		√ ∑f

= √ 2.67

= 1.63

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	4	4	6	11	6	5	5

Answer: 1.77

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	4 4 6 11 6 5 5	32 36 60 121 72 65 70	-3 -2 -1 0 1 2 3	-12 -8 -6 0 6 10 15	36 16 6 0 6 20 45
	∑f =41	∑fx=456	∑d=0	∑fd= 5	∑fd²129

Arithmetric mean	xbar	=	∑ fx	=	456	=	11.12
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{129}{41}$
		√ ∑f

= √ 3.15

= 1.77

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

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

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 4 5 13 5 5 4	21 32 45 130 55 60 52	-3 -2 -1 0 1 2 3	-9 -8 -5 0 5 10 12	27 16 5 0 5 20 36
	∑f =39	∑fx=395	∑d=0	∑fd= 5	∑fd²109

Arithmetric mean	xbar	=	∑ fx	=	395	=	10.13
			∑ f		39

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{109}{39}$
		√ ∑f

= √ 2.79

= 1.67

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

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

Answer: 1.68

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	3 6 9 12 7 6 5	24 54 90 132 84 78 70	-3 -2 -1 0 1 2 3	-9 -12 -9 0 7 12 15	27 24 9 0 7 24 45
	∑f =48	∑fx=532	∑d=0	∑fd= 4	∑fd²136

Arithmetric mean	xbar	=	∑ fx	=	532	=	11.08
			∑ f		48

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{136}{48}$
		√ ∑f

= √ 2.83

= 1.68

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	6	5	15	5	3	3

Answer: 1.58

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	3 6 5 15 5 3 3	24 54 50 165 60 39 42	-3 -2 -1 0 1 2 3	-9 -12 -5 0 5 6 9	27 24 5 0 5 12 27
	∑f =40	∑fx=434	∑d=0	∑fd= -6	∑fd²100

Arithmetric mean	xbar	=	∑ fx	=	434	=	10.85
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{100}{40}$
		√ ∑f

= √ 2.50

= 1.58

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

data x	10	11	12	13	14	15	16
frequency f	3	8	7	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 8 7 12 7 4 5	30 88 84 156 98 60 80	-3 -2 -1 0 1 2 3	-9 -16 -7 0 7 8 15	27 32 7 0 7 16 45
	∑f =46	∑fx=596	∑d=0	∑fd= -2	∑fd²134

Arithmetric mean	xbar	=	∑ fx	=	596	=	12.96
			∑ f		46

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{134}{46}$
		√ ∑f

= √ 2.91

= 1.71

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

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

Answer: 1.70

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	4 7 6 15 6 3 5	36 70 66 180 78 42 75	-3 -2 -1 0 1 2 3	-12 -14 -6 0 6 6 15	36 28 6 0 6 12 45
	∑f =46	∑fx=547	∑d=0	∑fd= -5	∑fd²133

Arithmetric mean	xbar	=	∑ fx	=	547	=	11.89
			∑ f		46

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{133}{46}$
		√ ∑f

= √ 2.89

= 1.70

10)

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

data x	10	11	12	13	14	15	16
frequency f	2	7	6	12	7	4	5

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	2 7 6 12 7 4 5	20 77 72 156 98 60 80	-3 -2 -1 0 1 2 3	-6 -14 -6 0 7 8 15	18 28 6 0 7 16 45
	∑f =43	∑fx=563	∑d=0	∑fd= 4	∑fd²120

Arithmetric mean	xbar	=	∑ fx	=	563	=	13.09
			∑ f		43

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{120}{43}$
		√ ∑f

= √ 2.79

= 1.67