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

Answer:_______________

The following table shows the marks obtained by 41 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer:_______________

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

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

Answer:_______________

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	7	5	14	5	4	3

Answer:_______________

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

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

Answer:_______________

The following table shows the marks obtained by 49 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer:_______________

10)

The following table shows the marks obtained by 41 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

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	4	6	9	11	7	5	4

Answer: 1.69

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	4 6 9 11 7 5 4	40 66 108 143 98 75 64	-3 -2 -1 0 1 2 3	-12 -12 -9 0 7 10 12	36 24 9 0 7 20 36
	∑f =46	∑fx=594	∑d=0	∑fd= -4	∑fd²132

Arithmetric mean	xbar	=	∑ fx	=	594	=	12.91
			∑ f		46

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{132}{46}$
		√ ∑f

= √ 2.87

= 1.69

The following table shows the marks obtained by 41 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.62

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	2 6 7 11 7 4 4	20 66 84 143 98 60 64	-3 -2 -1 0 1 2 3	-6 -12 -7 0 7 8 12	18 24 7 0 7 16 36
	∑f =41	∑fx=535	∑d=0	∑fd= 2	∑fd²108

Arithmetric mean	xbar	=	∑ fx	=	535	=	13.05
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{108}{41}$
		√ ∑f

= √ 2.63

= 1.62

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	6	7	10	6	4	5

Answer: 1.75

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 6 7 10 6 4 5	21 48 63 100 66 48 65	-3 -2 -1 0 1 2 3	-9 -12 -7 0 6 8 15	27 24 7 0 6 16 45
	∑f =41	∑fx=411	∑d=0	∑fd= 1	∑fd²125

Arithmetric mean	xbar	=	∑ fx	=	411	=	10.02
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{125}{41}$
		√ ∑f

= √ 3.05

= 1.75

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

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

Answer: 1.75

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 10	fd	fd²

7 8 9 10 11 12 13	3 6 5 10 5 4 4	21 48 45 100 55 48 52	-3 -2 -1 0 1 2 3	-9 -12 -5 0 5 8 12	27 24 5 0 5 16 36
	∑f =37	∑fx=369	∑d=0	∑fd= -1	∑fd²113

Arithmetric mean	xbar	=	∑ fx	=	369	=	9.97
			∑ f		37

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{113}{37}$
		√ ∑f

= √ 3.05

= 1.75

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	7	5	14	5	4	3

Answer: 1.57

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 14	fd	fd²

11 12 13 14 15 16 17	2 7 5 14 5 4 3	22 84 65 196 75 64 51	-3 -2 -1 0 1 2 3	-6 -14 -5 0 5 8 9	18 28 5 0 5 16 27
	∑f =40	∑fx=557	∑d=0	∑fd= -3	∑fd²99

Arithmetric mean	xbar	=	∑ fx	=	557	=	13.93
			∑ f		40

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{99}{40}$
		√ ∑f

= √ 2.48

= 1.57

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

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

Answer: 1.67

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	4 7 9 15 5 2 5	32 63 90 165 60 26 70	-3 -2 -1 0 1 2 3	-12 -14 -9 0 5 4 15	36 28 9 0 5 8 45
	∑f =47	∑fx=506	∑d=0	∑fd= -11	∑fd²131

Arithmetric mean	xbar	=	∑ fx	=	506	=	10.77
			∑ f		47

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{131}{47}$
		√ ∑f

= √ 2.79

= 1.67

The following table shows the marks obtained by 49 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.68

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	3 7 9 14 5 6 5	30 77 108 182 70 90 80	-3 -2 -1 0 1 2 3	-9 -14 -9 0 5 12 15	27 28 9 0 5 24 45
	∑f =49	∑fx=637	∑d=0	∑fd= 0	∑fd²138

Arithmetric mean	xbar	=	∑ fx	=	637	=	13.00
			∑ f		49

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{138}{49}$
		√ ∑f

= √ 2.82

= 1.68

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	3	7	7	12	7	2	4

Answer: 1.64

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 11	fd	fd²

8 9 10 11 12 13 14	3 7 7 12 7 2 4	24 63 70 132 84 26 56	-3 -2 -1 0 1 2 3	-9 -14 -7 0 7 4 12	27 28 7 0 7 8 36
	∑f =42	∑fx=455	∑d=0	∑fd= -7	∑fd²113

Arithmetric mean	xbar	=	∑ fx	=	455	=	10.83
			∑ f		42

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{113}{42}$
		√ ∑f

= √ 2.69

= 1.64

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

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

Answer: 1.64

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	2 8 9 13 5 3 5	20 88 108 169 70 45 80	-3 -2 -1 0 1 2 3	-6 -16 -9 0 5 6 15	18 32 9 0 5 12 45
	∑f =45	∑fx=580	∑d=0	∑fd= -5	∑fd²121

Arithmetric mean	xbar	=	∑ fx	=	580	=	12.89
			∑ f		45

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{121}{45}$
		√ ∑f

= √ 2.69

= 1.64

10)

The following table shows the marks obtained by 41 students in a Quiz competition in Mathematics. Calculate the stadard deviation.

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

Answer: 1.47

SOLUTION 1 :

x	f	fx	d = x-xbar = x - 13	fd	fd²

10 11 12 13 14 15 16	2 5 8 14 7 2 3	20 55 96 182 98 30 48	-3 -2 -1 0 1 2 3	-6 -10 -8 0 7 4 9	18 20 8 0 7 8 27
	∑f =41	∑fx=529	∑d=0	∑fd= -4	∑fd²88

Arithmetric mean	xbar	=	∑ fx	=	529	=	12.90
			∑ f		41

standard deviation Ô	=	√ ∑fd²	=	√ $\frac{88}{41}$
		√ ∑f

= √ 2.15

= 1.47