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

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

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	7	7	10	7	6	3

Answer:_______________

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

data x	9	10	11	12	13	14	15
frequency f	3	4	9	15	6	5	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	2	6	8	11	7	5	3

Answer:_______________

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

data x	11	12	13	14	15	16	17
frequency f	4	8	5	15	6	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	9	10	11	12	13	14	15
frequency f	4	6	7	12	5	6	3

Answer:_______________

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

data x	11	12	13	14	15	16	17
frequency f	2	7	9	11	6	3	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	3	6	5	12	7	2	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	3	8	8	13	5	5	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	11	12	13	14	15	16	17
frequency f	3	4	6	14	6	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	8	9	10	11	12	13	14
frequency f	2	4	5	15	6	5	5

Answer: 1.62

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	2 4 5 15 6 5 5	16 36 50 165 72 65 70	-3 -2 -1 0 1 2 3	-6 -8 -5 0 6 10 15	18 16 5 0 6 20 45
	∑f =42	∑fx=474	∑d=0	∑fd= 12	∑fd²110

Arithmetric mean	xbar	=	∑ fx	=	474	=	11.29
			∑ f		42

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{110}{42}$
		√ ∑f

= √ 2.62

= 1.62

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	7	7	10	7	6	3

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 7 7 10 7 6 3	21 56 63 100 77 72 39	-3 -2 -1 0 1 2 3	-9 -14 -7 0 7 12 9	27 28 7 0 7 24 27
	∑f =43	∑fx=428	∑d=0	∑fd= -2	∑fd²120

Arithmetric mean	xbar	=	∑ fx	=	428	=	9.95
			∑ f		43

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

= √ 2.79

= 1.67

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

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

Answer: 1.53

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	3 4 9 15 6 5 3	27 40 99 180 78 70 45	-3 -2 -1 0 1 2 3	-9 -8 -9 0 6 10 9	27 16 9 0 6 20 27
	∑f =45	∑fx=539	∑d=0	∑fd= -1	∑fd²105

Arithmetric mean	xbar	=	∑ fx	=	539	=	11.98
			∑ f		45

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{105}{45}$
		√ ∑f

= √ 2.33

= 1.53

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	8	11	7	5	3

Answer: 1.57

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	2 6 8 11 7 5 3	14 48 72 110 77 60 39	-3 -2 -1 0 1 2 3	-6 -12 -8 0 7 10 9	18 24 8 0 7 20 27
	∑f =42	∑fx=420	∑d=0	∑fd= 0	∑fd²104

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

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{104}{42}$
		√ ∑f

= √ 2.48

= 1.57

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

data x	11	12	13	14	15	16	17
frequency f	4	8	5	15	6	4	3

Answer: 1.65

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	4 8 5 15 6 4 3	44 96 65 210 90 64 51	-3 -2 -1 0 1 2 3	-12 -16 -5 0 6 8 9	36 32 5 0 6 16 27
	∑f =45	∑fx=620	∑d=0	∑fd= -10	∑fd²122

Arithmetric mean	xbar	=	∑ fx	=	620	=	13.78
			∑ f		45

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{122}{45}$
		√ ∑f

= √ 2.71

= 1.65

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

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

Answer: 1.69

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	4 6 7 12 5 6 3	36 60 77 144 65 84 45	-3 -2 -1 0 1 2 3	-12 -12 -7 0 5 12 9	36 24 7 0 5 24 27
	∑f =43	∑fx=511	∑d=0	∑fd= -5	∑fd²123

Arithmetric mean	xbar	=	∑ fx	=	511	=	11.88
			∑ f		43

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{123}{43}$
		√ ∑f

= √ 2.86

= 1.69

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

data x	11	12	13	14	15	16	17
frequency f	2	7	9	11	6	3	5

Answer: 1.66

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	2 7 9 11 6 3 5	22 84 117 154 90 48 85	-3 -2 -1 0 1 2 3	-6 -14 -9 0 6 6 15	18 28 9 0 6 12 45
	∑f =43	∑fx=600	∑d=0	∑fd= -2	∑fd²118

Arithmetric mean	xbar	=	∑ fx	=	600	=	13.95
			∑ f		43

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{118}{43}$
		√ ∑f

= √ 2.74

= 1.66

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	3	6	5	12	7	2	3

Answer: 1.61

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	3 6 5 12 7 2 3	33 72 65 168 105 32 51	-3 -2 -1 0 1 2 3	-9 -12 -5 0 7 4 9	27 24 5 0 7 8 27
	∑f =38	∑fx=526	∑d=0	∑fd= -6	∑fd²98

Arithmetric mean	xbar	=	∑ fx	=	526	=	13.84
			∑ f		38

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{98}{38}$
		√ ∑f

= √ 2.58

= 1.61

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	3	8	8	13	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	3 8 8 13 5 5 5	21 64 72 130 55 60 65	-3 -2 -1 0 1 2 3	-9 -16 -8 0 5 10 15	27 32 8 0 5 20 45
	∑f =47	∑fx=467	∑d=0	∑fd= -3	∑fd²137

Arithmetric mean	xbar	=	∑ fx	=	467	=	9.94
			∑ f		47

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

= √ 2.91

= 1.71

10)

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

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

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	3 4 6 14 6 5 5	33 48 78 196 90 80 85	-3 -2 -1 0 1 2 3	-9 -8 -6 0 6 10 15	27 16 6 0 6 20 45
	∑f =43	∑fx=610	∑d=0	∑fd= 8	∑fd²120

Arithmetric mean	xbar	=	∑ fx	=	610	=	14.19
			∑ f		43

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

= √ 2.79

= 1.67