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	8	9	10	11	12	13	14
frequency f	2	4	7	14	7	2	4

Answer:_______________

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

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

Answer:_______________

The following table shows the marks obtained by 39 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	11	7	4	3

Answer:_______________

The following table shows the marks obtained by 43 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	14	5	6	3

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	6	10	7	4	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	5	6	11	6	4	4

Answer:_______________

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

data x	10	11	12	13	14	15	16
frequency f	3	6	5	11	5	3	3

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	4	5	7	11	6	3	3

Answer:_______________

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

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

Answer:_______________

10)

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

data x	11	12	13	14	15	16	17
frequency f	2	6	7	10	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	8	9	10	11	12	13	14
frequency f	2	4	7	14	7	2	4

Answer: 1.52

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	2 4 7 14 7 2 4	16 36 70 154 84 26 56	-3 -2 -1 0 1 2 3	-6 -8 -7 0 7 4 12	18 16 7 0 7 8 36
	∑f =40	∑fx=442	∑d=0	∑fd= 2	∑fd²92

Arithmetric mean	xbar	=	∑ fx	=	442	=	11.05
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{92}{40}$
		√ ∑f

= √ 2.30

= 1.52

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

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

Answer: 1.61

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	2 8 9 11 6 6 3	16 72 90 121 72 78 42	-3 -2 -1 0 1 2 3	-6 -16 -9 0 6 12 9	18 32 9 0 6 24 27
	∑f =45	∑fx=491	∑d=0	∑fd= -4	∑fd²116

Arithmetric mean	xbar	=	∑ fx	=	491	=	10.91
			∑ f		45

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{116}{45}$
		√ ∑f

= √ 2.58

= 1.61

The following table shows the marks obtained by 39 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	11	7	4	3

Answer: 1.56

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	2 5 7 11 7 4 3	20 55 84 143 98 60 48	-3 -2 -1 0 1 2 3	-6 -10 -7 0 7 8 9	18 20 7 0 7 16 27
	∑f =39	∑fx=508	∑d=0	∑fd= 1	∑fd²95

Arithmetric mean	xbar	=	∑ fx	=	508	=	13.03
			∑ f		39

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{95}{39}$
		√ ∑f

= √ 2.44

= 1.56

The following table shows the marks obtained by 43 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	14	5	6	3

Answer: 1.62

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 6 6 14 5 6 3	21 48 54 140 55 72 39	-3 -2 -1 0 1 2 3	-9 -12 -6 0 5 12 9	27 24 6 0 5 24 27
	∑f =43	∑fx=429	∑d=0	∑fd= -1	∑fd²113

Arithmetric mean	xbar	=	∑ fx	=	429	=	9.98
			∑ f		43

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{113}{43}$
		√ ∑f

= √ 2.63

= 1.62

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	6	10	7	4	5

Answer: 1.79

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	4 6 6 10 7 4 5	28 48 54 100 77 48 65	-3 -2 -1 0 1 2 3	-12 -12 -6 0 7 8 15	36 24 6 0 7 16 45
	∑f =42	∑fx=420	∑d=0	∑fd= 0	∑fd²134

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

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{134}{42}$
		√ ∑f

= √ 3.19

= 1.79

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	5	6	11	6	4	4

Answer: 1.69

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 5 6 11 6 4 4	21 40 54 110 66 48 52	-3 -2 -1 0 1 2 3	-9 -10 -6 0 6 8 12	27 20 6 0 6 16 36
	∑f =39	∑fx=391	∑d=0	∑fd= 1	∑fd²111

Arithmetric mean	xbar	=	∑ fx	=	391	=	10.03
			∑ f		39

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{111}{39}$
		√ ∑f

= √ 2.85

= 1.69

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

data x	10	11	12	13	14	15	16
frequency f	3	6	5	11	5	3	3

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	3 6 5 11 5 3 3	30 66 60 143 70 45 48	-3 -2 -1 0 1 2 3	-9 -12 -5 0 5 6 9	27 24 5 0 5 12 27
	∑f =36	∑fx=462	∑d=0	∑fd= -6	∑fd²100

Arithmetric mean	xbar	=	∑ fx	=	462	=	12.83
			∑ f		36

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{100}{36}$
		√ ∑f

= √ 2.78

= 1.67

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	4	5	7	11	6	3	3

Answer: 1.66

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	4 5 7 11 6 3 3	28 40 63 110 66 36 39	-3 -2 -1 0 1 2 3	-12 -10 -7 0 6 6 9	36 20 7 0 6 12 27
	∑f =39	∑fx=382	∑d=0	∑fd= -8	∑fd²108

Arithmetric mean	xbar	=	∑ fx	=	382	=	9.79
			∑ f		39

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{108}{39}$
		√ ∑f

= √ 2.77

= 1.66

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

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

Answer: 1.71

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	4 6 7 15 5 5 5	28 48 63 150 55 60 65	-3 -2 -1 0 1 2 3	-12 -12 -7 0 5 10 15	36 24 7 0 5 20 45
	∑f =47	∑fx=469	∑d=0	∑fd= -1	∑fd²137

Arithmetric mean	xbar	=	∑ fx	=	469	=	9.98
			∑ f		47

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{137}{47}$
		√ ∑f

= √ 2.91

= 1.71

10)

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

data x	11	12	13	14	15	16	17
frequency f	2	6	7	10	6	5	4

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	2 6 7 10 6 5 4	22 72 91 140 90 80 68	-3 -2 -1 0 1 2 3	-6 -12 -7 0 6 10 12	18 24 7 0 6 20 36
	∑f =40	∑fx=563	∑d=0	∑fd= 3	∑fd²111

Arithmetric mean	xbar	=	∑ fx	=	563	=	14.08
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{111}{40}$
		√ ∑f

= √ 2.78

= 1.67