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 40 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	10	5	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	5	9	14	5	6	3

Answer:_______________

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

data x	9	10	11	12	13	14	15
frequency f	2	8	9	15	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	7	8	9	10	11	12	13
frequency f	3	6	6	10	6	5	5

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	3	7	7	10	6	5	3

Answer:_______________

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

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

Answer:_______________

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

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

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	7	12	5	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	2	6	6	15	6	3	4

Answer:_______________

10)

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

data x	10	11	12	13	14	15	16
frequency f	2	5	7	15	5	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	6	8	10	5	4	5

Answer: 1.70

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	2 6 8 10 5 4 5	14 48 72 100 55 48 65	-3 -2 -1 0 1 2 3	-6 -12 -8 0 5 8 15	18 24 8 0 5 16 45
	∑f =40	∑fx=402	∑d=0	∑fd= 2	∑fd²116

Arithmetric mean	xbar	=	∑ fx	=	402	=	10.05
			∑ f		40

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

= √ 2.90

= 1.70

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	5	9	14	5	6	3

Answer: 1.62

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	4 5 9 14 5 6 3	36 50 99 168 65 84 45	-3 -2 -1 0 1 2 3	-12 -10 -9 0 5 12 9	36 20 9 0 5 24 27
	∑f =46	∑fx=547	∑d=0	∑fd= -5	∑fd²121

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

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

= √ 2.63

= 1.62

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

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

Answer: 1.49

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	2 8 9 15 7 3 3	18 80 99 180 91 42 45	-3 -2 -1 0 1 2 3	-6 -16 -9 0 7 6 9	18 32 9 0 7 12 27
	∑f =47	∑fx=555	∑d=0	∑fd= -9	∑fd²105

Arithmetric mean	xbar	=	∑ fx	=	555	=	11.81
			∑ f		47

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{105}{47}$
		√ ∑f

= √ 2.23

= 1.49

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	3	6	6	10	6	5	5

Answer: 1.77

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 6 6 10 6 5 5	21 48 54 100 66 60 65	-3 -2 -1 0 1 2 3	-9 -12 -6 0 6 10 15	27 24 6 0 6 20 45
	∑f =41	∑fx=414	∑d=0	∑fd= 4	∑fd²128

Arithmetric mean	xbar	=	∑ fx	=	414	=	10.10
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{128}{41}$
		√ ∑f

= √ 3.12

= 1.77

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	3	7	7	10	6	5	3

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	3 7 7 10 6 5 3	33 84 91 140 90 80 51	-3 -2 -1 0 1 2 3	-9 -14 -7 0 6 10 9	27 28 7 0 6 20 27
	∑f =41	∑fx=569	∑d=0	∑fd= -5	∑fd²115

Arithmetric mean	xbar	=	∑ fx	=	569	=	13.88
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{115}{41}$
		√ ∑f

= √ 2.80

= 1.67

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

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

Answer: 1.70

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	2 6 5 10 5 4 4	16 54 50 110 60 52 56	-3 -2 -1 0 1 2 3	-6 -12 -5 0 5 8 12	18 24 5 0 5 16 36
	∑f =36	∑fx=398	∑d=0	∑fd= 2	∑fd²104

Arithmetric mean	xbar	=	∑ fx	=	398	=	11.06
			∑ f		36

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{104}{36}$
		√ ∑f

= √ 2.89

= 1.70

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

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

Answer: 1.71

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	4 6 8 14 5 5 5	44 72 104 196 75 80 85	-3 -2 -1 0 1 2 3	-12 -12 -8 0 5 10 15	36 24 8 0 5 20 45
	∑f =47	∑fx=656	∑d=0	∑fd= -2	∑fd²138

Arithmetric mean	xbar	=	∑ fx	=	656	=	13.96
			∑ f		47

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{138}{47}$
		√ ∑f

= √ 2.94

= 1.71

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	7	12	5	6	5

Answer: 1.74

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	3 7 7 12 5 6 5	30 77 84 156 70 90 80	-3 -2 -1 0 1 2 3	-9 -14 -7 0 5 12 15	27 28 7 0 5 24 45
	∑f =45	∑fx=587	∑d=0	∑fd= 2	∑fd²136

Arithmetric mean	xbar	=	∑ fx	=	587	=	13.04
			∑ f		45

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{136}{45}$
		√ ∑f

= √ 3.02

= 1.74

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	2	6	6	15	6	3	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 6 15 6 3 4	14 48 54 150 66 36 52	-3 -2 -1 0 1 2 3	-6 -12 -6 0 6 6 12	18 24 6 0 6 12 36
	∑f =42	∑fx=420	∑d=0	∑fd= 0	∑fd²102

Arithmetric mean	xbar	=	∑ fx	=	420	=	10.00
			∑ f		42

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{102}{42}$
		√ ∑f

= √ 2.43

= 1.56

10)

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

data x	10	11	12	13	14	15	16
frequency f	2	5	7	15	5	3	4

Answer: 1.55

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	2 5 7 15 5 3 4	20 55 84 195 70 45 64	-3 -2 -1 0 1 2 3	-6 -10 -7 0 5 6 12	18 20 7 0 5 12 36
	∑f =41	∑fx=533	∑d=0	∑fd= 0	∑fd²98

Arithmetric mean	xbar	=	∑ fx	=	533	=	13.00
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{98}{41}$
		√ ∑f

= √ 2.39

= 1.55