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

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

Answer:_______________

The following table shows the marks obtained by 46 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

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	7	7	10	5	5	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	4	5	9	10	7	5	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	7	13	6	6	4

Answer:_______________

The following table shows the marks obtained by 42 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	13	6	3	4

Answer:_______________

The following table shows the marks obtained by 37 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer:_______________

The following table shows the marks obtained by 38 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

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	2	5	5	11	7	5	3

Answer:_______________

10)

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	3	4	6	13	5	4	4

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	5	7	13	6	6	5

Answer: 1.73

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	4 5 7 13 6 6 5	44 60 91 182 90 96 85	-3 -2 -1 0 1 2 3	-12 -10 -7 0 6 12 15	36 20 7 0 6 24 45
	∑f =46	∑fx=648	∑d=0	∑fd= 4	∑fd²138

Arithmetric mean	xbar	=	∑ fx	=	648	=	14.09
			∑ f		46

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

= √ 3.00

= 1.73

The following table shows the marks obtained by 46 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.63

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	3 8 9 12 7 3 4	30 88 108 156 98 45 64	-3 -2 -1 0 1 2 3	-9 -16 -9 0 7 6 12	27 32 9 0 7 12 36
	∑f =46	∑fx=589	∑d=0	∑fd= -9	∑fd²123

Arithmetric mean	xbar	=	∑ fx	=	589	=	12.80
			∑ f		46

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

= √ 2.67

= 1.63

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	7	7	10	5	5	3

Answer: 1.64

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	2 7 7 10 5 5 3	20 77 84 130 70 75 48	-3 -2 -1 0 1 2 3	-6 -14 -7 0 5 10 9	18 28 7 0 5 20 27
	∑f =39	∑fx=504	∑d=0	∑fd= -3	∑fd²105

Arithmetric mean	xbar	=	∑ fx	=	504	=	12.92
			∑ f		39

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{105}{39}$
		√ ∑f

= √ 2.69

= 1.64

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	4	5	9	10	7	5	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 9 10 7 5 3	28 40 81 100 77 60 39	-3 -2 -1 0 1 2 3	-12 -10 -9 0 7 10 9	36 20 9 0 7 20 27
	∑f =43	∑fx=425	∑d=0	∑fd= -5	∑fd²119

Arithmetric mean	xbar	=	∑ fx	=	425	=	9.88
			∑ f		43

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{119}{43}$
		√ ∑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	3	8	7	13	6	6	4

Answer: 1.68

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 8 7 13 6 6 4	21 64 63 130 66 72 52	-3 -2 -1 0 1 2 3	-9 -16 -7 0 6 12 12	27 32 7 0 6 24 36
	∑f =47	∑fx=468	∑d=0	∑fd= -2	∑fd²132

Arithmetric mean	xbar	=	∑ fx	=	468	=	9.96
			∑ f		47

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{132}{47}$
		√ ∑f

= √ 2.81

= 1.68

The following table shows the marks obtained by 42 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	13	6	3	4

Answer: 1.62

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 12	fd	fd²

9 10 11 12 13 14 15	2 8 6 13 6 3 4	18 80 66 156 78 42 60	-3 -2 -1 0 1 2 3	-6 -16 -6 0 6 6 12	18 32 6 0 6 12 36
	∑f =42	∑fx=500	∑d=0	∑fd= -4	∑fd²110

Arithmetric mean	xbar	=	∑ fx	=	500	=	11.90
			∑ f		42

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

= √ 2.62

= 1.62

The following table shows the marks obtained by 37 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.65

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	2 4 6 11 5 5 4	16 36 60 121 60 65 56	-3 -2 -1 0 1 2 3	-6 -8 -6 0 5 10 12	18 16 6 0 5 20 36
	∑f =37	∑fx=414	∑d=0	∑fd= 7	∑fd²101

Arithmetric mean	xbar	=	∑ fx	=	414	=	11.19
			∑ f		37

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{101}{37}$
		√ ∑f

= √ 2.73

= 1.65

The following table shows the marks obtained by 38 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.62

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	2 8 5 11 6 3 3	14 64 45 110 66 36 39	-3 -2 -1 0 1 2 3	-6 -16 -5 0 6 6 9	18 32 5 0 6 12 27
	∑f =38	∑fx=374	∑d=0	∑fd= -6	∑fd²100

Arithmetric mean	xbar	=	∑ fx	=	374	=	9.84
			∑ f		38

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{100}{38}$
		√ ∑f

= √ 2.63

= 1.62

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	2	5	5	11	7	5	3

Answer: 1.60

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	2 5 5 11 7 5 3	22 60 65 154 105 80 51	-3 -2 -1 0 1 2 3	-6 -10 -5 0 7 10 9	18 20 5 0 7 20 27
	∑f =38	∑fx=537	∑d=0	∑fd= 5	∑fd²97

Arithmetric mean	xbar	=	∑ fx	=	537	=	14.13
			∑ f		38

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{97}{38}$
		√ ∑f

= √ 2.55

= 1.60

10)

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	3	4	6	13	5	4	4

Answer: 1.65

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	3 4 6 13 5 4 4	30 44 72 169 70 60 64	-3 -2 -1 0 1 2 3	-9 -8 -6 0 5 8 12	27 16 6 0 5 16 36
	∑f =39	∑fx=509	∑d=0	∑fd= 2	∑fd²106

Arithmetric mean	xbar	=	∑ fx	=	509	=	13.05
			∑ f		39

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{106}{39}$
		√ ∑f

= √ 2.72

= 1.65