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

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

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	4	4	8	13	6	2	4

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	2	8	7	15	5	4	5

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	2	8	6	12	7	6	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	4	5	14	6	4	5

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

Answer:_______________

10)

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	8	8	15	5	2	3

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	3	7	9	10	6	5	3

Answer: 1.65

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	3 7 9 10 6 5 3	24 63 90 110 72 65 42	-3 -2 -1 0 1 2 3	-9 -14 -9 0 6 10 9	27 28 9 0 6 20 27
	∑f =43	∑fx=466	∑d=0	∑fd= -7	∑fd²117

Arithmetric mean	xbar	=	∑ fx	=	466	=	10.84
			∑ f		43

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{117}{43}$
		√ ∑f

= √ 2.72

= 1.65

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	4	6	6	13	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	4 6 6 13 7 5 5	44 72 78 182 105 80 85	-3 -2 -1 0 1 2 3	-12 -12 -6 0 7 10 15	36 24 6 0 7 20 45
	∑f =46	∑fx=646	∑d=0	∑fd= 2	∑fd²138

Arithmetric mean	xbar	=	∑ fx	=	646	=	14.04
			∑ f		46

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{138}{46}$
		√ ∑f

= √ 3.00

= 1.73

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	4	8	8	14	6	4	4

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	4 8 8 14 6 4 4	32 72 80 154 72 52 56	-3 -2 -1 0 1 2 3	-12 -16 -8 0 6 8 12	36 32 8 0 6 16 36
	∑f =48	∑fx=518	∑d=0	∑fd= -10	∑fd²134

Arithmetric mean	xbar	=	∑ fx	=	518	=	10.79
			∑ f		48

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{134}{48}$
		√ ∑f

= √ 2.79

= 1.67

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	4	4	8	13	6	2	4

Answer: 1.64

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	4 4 8 13 6 2 4	44 48 104 182 90 32 68	-3 -2 -1 0 1 2 3	-12 -8 -8 0 6 4 12	36 16 8 0 6 8 36
	∑f =41	∑fx=568	∑d=0	∑fd= -6	∑fd²110

Arithmetric mean	xbar	=	∑ fx	=	568	=	13.85
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{110}{41}$
		√ ∑f

= √ 2.68

= 1.64

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	2	8	7	15	5	4	5

Answer: 1.63

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	2 8 7 15 5 4 5	18 80 77 180 65 56 75	-3 -2 -1 0 1 2 3	-6 -16 -7 0 5 8 15	18 32 7 0 5 16 45
	∑f =46	∑fx=551	∑d=0	∑fd= -1	∑fd²123

Arithmetric mean	xbar	=	∑ fx	=	551	=	11.98
			∑ f		46

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{123}{46}$
		√ ∑f

= √ 2.67

= 1.63

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	2	8	6	12	7	6	3

Answer: 1.61

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	2 8 6 12 7 6 3	18 80 66 144 91 84 45	-3 -2 -1 0 1 2 3	-6 -16 -6 0 7 12 9	18 32 6 0 7 24 27
	∑f =44	∑fx=528	∑d=0	∑fd= 0	∑fd²114

Arithmetric mean	xbar	=	∑ fx	=	528	=	12.00
			∑ f		44

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{114}{44}$
		√ ∑f

= √ 2.59

= 1.61

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	4	5	14	6	4	5

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 14 6 4 5	21 32 45 140 66 48 65	-3 -2 -1 0 1 2 3	-9 -8 -5 0 6 8 15	27 16 5 0 6 16 45
	∑f =41	∑fx=417	∑d=0	∑fd= 7	∑fd²115

Arithmetric mean	xbar	=	∑ fx	=	417	=	10.17
			∑ f		41

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

= √ 2.80

= 1.67

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	2	7	6	14	6	5	4

Answer: 1.61

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	2 7 6 14 6 5 4	18 70 66 168 78 70 60	-3 -2 -1 0 1 2 3	-6 -14 -6 0 6 10 12	18 28 6 0 6 20 36
	∑f =44	∑fx=530	∑d=0	∑fd= 2	∑fd²114

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

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{114}{44}$
		√ ∑f

= √ 2.59

= 1.61

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	7	6	13	5	3	3

Answer: 1.62

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	3 7 6 13 5 3 3	27 70 66 156 65 42 45	-3 -2 -1 0 1 2 3	-9 -14 -6 0 5 6 9	27 28 6 0 5 12 27
	∑f =40	∑fx=471	∑d=0	∑fd= -9	∑fd²105

Arithmetric mean	xbar	=	∑ fx	=	471	=	11.78
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{105}{40}$
		√ ∑f

= √ 2.63

= 1.62

10)

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	8	8	15	5	2	3

Answer: 1.56

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	3 8 8 15 5 2 3	24 72 80 165 60 26 42	-3 -2 -1 0 1 2 3	-9 -16 -8 0 5 4 9	27 32 8 0 5 8 27
	∑f =44	∑fx=469	∑d=0	∑fd= -15	∑fd²107

Arithmetric mean	xbar	=	∑ fx	=	469	=	10.66
			∑ f		44

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{107}{44}$
		√ ∑f

= √ 2.43

= 1.56