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

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

Answer:_______________

The following table shows the marks obtained by 50 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer:_______________

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

data x	10	11	12	13	14	15	16
frequency f	4	4	9	14	7	6	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	4	5	7	12	5	2	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	9	12	6	5	4

Answer:_______________

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

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

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	3	7	8	14	7	4	4

Answer:_______________

The following table shows the marks obtained by 44 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	13	7	5	5

Answer:_______________

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

data x	10	11	12	13	14	15	16
frequency f	2	6	5	13	7	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	8	9	10	11	12	13	14
frequency f	4	6	7	11	6	6	4

Answer:_______________

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

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

Answer: 1.58

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	2 4 7 12 5 2 4	14 32 63 120 55 24 52	-3 -2 -1 0 1 2 3	-6 -8 -7 0 5 4 12	18 16 7 0 5 8 36
	∑f =36	∑fx=360	∑d=0	∑fd= 0	∑fd²90

Arithmetric mean	xbar	=	∑ fx	=	360	=	10.00
			∑ f		36

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{90}{36}$
		√ ∑f

= √ 2.50

= 1.58

The following table shows the marks obtained by 50 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	3 8 9 14 6 5 5	24 72 90 154 72 65 70	-3 -2 -1 0 1 2 3	-9 -16 -9 0 6 10 15	27 32 9 0 6 20 45
	∑f =50	∑fx=547	∑d=0	∑fd= -3	∑fd²139

Arithmetric mean	xbar	=	∑ fx	=	547	=	10.94
			∑ f		50

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{139}{50}$
		√ ∑f

= √ 2.78

= 1.67

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

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

Answer: 1.59

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	4 4 9 14 7 6 3	40 44 108 182 98 90 48	-3 -2 -1 0 1 2 3	-12 -8 -9 0 7 12 9	36 16 9 0 7 24 27
	∑f =47	∑fx=610	∑d=0	∑fd= -1	∑fd²119

Arithmetric mean	xbar	=	∑ fx	=	610	=	12.98
			∑ f		47

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{119}{47}$
		√ ∑f

= √ 2.53

= 1.59

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	4	5	7	12	5	2	5

Answer: 1.74

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	4 5 7 12 5 2 5	32 45 70 132 60 26 70	-3 -2 -1 0 1 2 3	-12 -10 -7 0 5 4 15	36 20 7 0 5 8 45
	∑f =40	∑fx=435	∑d=0	∑fd= -5	∑fd²121

Arithmetric mean	xbar	=	∑ fx	=	435	=	10.88
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{121}{40}$
		√ ∑f

= √ 3.03

= 1.74

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	9	12	6	5	4

Answer: 1.70

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	4 8 9 12 6 5 4	32 72 90 132 72 65 56	-3 -2 -1 0 1 2 3	-12 -16 -9 0 6 10 12	36 32 9 0 6 20 36
	∑f =48	∑fx=519	∑d=0	∑fd= -9	∑fd²139

Arithmetric mean	xbar	=	∑ fx	=	519	=	10.81
			∑ f		48

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{139}{48}$
		√ ∑f

= √ 2.90

= 1.70

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

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

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	2 6 5 13 5 3 5	18 60 55 156 65 42 75	-3 -2 -1 0 1 2 3	-6 -12 -5 0 5 6 15	18 24 5 0 5 12 45
	∑f =39	∑fx=471	∑d=0	∑fd= 3	∑fd²109

Arithmetric mean	xbar	=	∑ fx	=	471	=	12.08
			∑ f		39

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

= √ 2.79

= 1.67

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	3	7	8	14	7	4	4

Answer: 1.61

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	3 7 8 14 7 4 4	33 84 104 196 105 64 68	-3 -2 -1 0 1 2 3	-9 -14 -8 0 7 8 12	27 28 8 0 7 16 36
	∑f =47	∑fx=654	∑d=0	∑fd= -4	∑fd²122

Arithmetric mean	xbar	=	∑ fx	=	654	=	13.91
			∑ f		47

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{122}{47}$
		√ ∑f

= √ 2.60

= 1.61

The following table shows the marks obtained by 44 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	13	7	5	5

Answer: 1.71

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	3 6 5 13 7 5 5	33 72 65 182 105 80 85	-3 -2 -1 0 1 2 3	-9 -12 -5 0 7 10 15	27 24 5 0 7 20 45
	∑f =44	∑fx=622	∑d=0	∑fd= 6	∑fd²128

Arithmetric mean	xbar	=	∑ fx	=	622	=	14.14
			∑ f		44

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{128}{44}$
		√ ∑f

= √ 2.91

= 1.71

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

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

Answer: 1.66

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	2 6 5 13 7 4 5	20 66 60 169 98 60 80	-3 -2 -1 0 1 2 3	-6 -12 -5 0 7 8 15	18 24 5 0 7 16 45
	∑f =42	∑fx=553	∑d=0	∑fd= 7	∑fd²115

Arithmetric mean	xbar	=	∑ fx	=	553	=	13.17
			∑ f		42

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{115}{42}$
		√ ∑f

= √ 2.74

= 1.66

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	4	6	7	11	6	6	4

Answer: 1.74

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	4 6 7 11 6 6 4	32 54 70 121 72 78 56	-3 -2 -1 0 1 2 3	-12 -12 -7 0 6 12 12	36 24 7 0 6 24 36
	∑f =44	∑fx=483	∑d=0	∑fd= -1	∑fd²133

Arithmetric mean	xbar	=	∑ fx	=	483	=	10.98
			∑ f		44

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{133}{44}$
		√ ∑f

= √ 3.02

= 1.74