Sasi Math (Revised for 1024)

Scroll:statistics >> standard deviation >> saq (4247)

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.

Calculate the standard deviation.

Natural numbers are 43,37,34,30,23,28,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,36,33,29,20,27,33

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,37,32,29,24,27,32

Answer:_______________

Calculate the standard deviation.

Natural numbers are 41,38,32,31,20,28,32

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,39,34,30,20,26,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,36,33,29,20,28,33

Answer:_______________

Calculate the standard deviation.

Natural numbers are 43,36,35,31,25,26,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 41,39,35,29,24,26,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 40,39,32,29,25,26,32

Answer:_______________

10)

Calculate the standard deviation.

Natural numbers are 43,37,35,29,20,26,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 43,37,34,30,23,28,34

Answer: 5.99

SOLUTION 1 :

Assumed Mean Method

Let us take A = 34 as assumed mean and form the following table.

x	d = x- 34	d²

23 28 30 34 34 37 43	-11 -6 -4 0 0 3 9	121 36 16 0 0 9 81
	∑d= -9	∑d² = 263

Here, n = 7

standard deviation Ô	=	√ ∑d²	-	√ (∑d)²
		√ n		√ n²

= √ $\frac{(263}{7)}$ - √ $\frac{(-9}{7}$ )²

= √ (37.57 - (-1.29)²)

= √ (37.57-1.66)

= √ 35.91

standard deviation Ô = 5.99

Calculate the standard deviation.

Natural numbers are 44,36,33,29,20,27,33

Answer: 6.96

SOLUTION 1 :

Assumed Mean Method

Let us take A = 33 as assumed mean and form the following table.

x	d = x- 33	d²

20 27 29 33 33 36 44	-13 -6 -4 0 0 3 11	169 36 16 0 0 9 121
	∑d= -9	∑d² = 351

Here, n = 7

standard deviation Ô	=	√ ∑d²	-	√ (∑d)²
		√ n		√ n²

= √ $\frac{(351}{7)}$ - √ $\frac{(-9}{7}$ )²

= √ (50.14 - (-1.29)²)

= √ (50.14-1.66)

= √ 48.48

standard deviation Ô = 6.96

Calculate the standard deviation.

Natural numbers are 44,37,32,29,24,27,32

Answer: 6.17

SOLUTION 1 :

Assumed Mean Method

Let us take A = 32 as assumed mean and form the following table.

x	d = x- 32	d²

24 27 29 32 32 37 44	-8 -5 -3 0 0 5 12	64 25 9 0 0 25 144
	∑d= 1	∑d² = 267

Here, n = 7

standard deviation Ô	=	√ ∑d²	-	√ (∑d)²
		√ n		√ n²

= √ $\frac{(267}{7)}$ - √ $\frac{(1}{7}$ )²

= √ (38.14 - (0.14)²)

= √ (38.14-0.02)

= √ 38.12

standard deviation Ô = 6.17

Calculate the standard deviation.

Natural numbers are 41,38,32,31,20,28,32

Answer: 6.30

SOLUTION 1 :

Assumed Mean Method

Let us take A = 32 as assumed mean and form the following table.

x	d = x- 32	d²

20 28 31 32 32 38 41	-12 -4 -1 0 0 6 9	144 16 1 0 0 36 81
	∑d= -2	∑d² = 278

Here, n = 7

standard deviation Ô	=	√ ∑d²	-	√ (∑d)²
		√ n		√ n²

= √ $\frac{(278}{7)}$ - √ $\frac{(-2}{7}$ )²

= √ (39.71 - (-0.29)²)

= √ (39.71-0.08)

= √ 39.63

standard deviation Ô = 6.30

Calculate the standard deviation.

Natural numbers are 44,39,34,30,20,26,34

Answer: 7.40

SOLUTION 1 :

Assumed Mean Method

Let us take A = 34 as assumed mean and form the following table.

x	d = x- 34	d²

20 26 30 34 34 39 44	-14 -8 -4 0 0 5 10	196 64 16 0 0 25 100
	∑d= -11	∑d² = 401

Here, n = 7

standard deviation Ô	=	√ ∑d²	-	√ (∑d)²
		√ n		√ n²

= √ $\frac{(401}{7)}$ - √ $\frac{(-11}{7}$ )²

= √ (57.29 - (-1.57)²)

= √ (57.29-2.46)

= √ 54.83

standard deviation Ô = 7.40

Calculate the standard deviation.

Natural numbers are 44,36,33,29,20,28,33

Answer: 6.88

SOLUTION 1 :

Assumed Mean Method

Let us take A = 33 as assumed mean and form the following table.

x	d = x- 33	d²

20 28 29 33 33 36 44	-13 -5 -4 0 0 3 11	169 25 16 0 0 9 121
	∑d= -8	∑d² = 340

Here, n = 7

standard deviation Ô	=	√ ∑d²	-	√ (∑d)²
		√ n		√ n²

= √ $\frac{(340}{7)}$ - √ $\frac{(-8}{7}$ )²

= √ (48.57 - (-1.14)²)

= √ (48.57-1.30)

= √ 47.27

standard deviation Ô = 6.88

Calculate the standard deviation.

Natural numbers are 43,36,35,31,25,26,35

Answer: 5.78

SOLUTION 1 :

Assumed Mean Method

Let us take A = 35 as assumed mean and form the following table.

x	d = x- 35	d²

25 26 31 35 35 36 43	-10 -9 -4 0 0 1 8	100 81 16 0 0 1 64
	∑d= -14	∑d² = 262

Here, n = 7

standard deviation Ô	=	√ ∑d²	-	√ (∑d)²
		√ n		√ n²

= √ $\frac{(262}{7)}$ - √ $\frac{(-14}{7}$ )²

= √ (37.43 - (-2.00)²)

= √ (37.43-4.00)

= √ 33.43

standard deviation Ô = 5.78

Calculate the standard deviation.

Natural numbers are 41,39,35,29,24,26,35

Answer: 6.02

SOLUTION 1 :

Assumed Mean Method

Let us take A = 35 as assumed mean and form the following table.

x	d = x- 35	d²

24 26 29 35 35 39 41	-11 -9 -6 0 0 4 6	121 81 36 0 0 16 36
	∑d= -16	∑d² = 290

Here, n = 7

standard deviation Ô	=	√ ∑d²	-	√ (∑d)²
		√ n		√ n²

= √ $\frac{(290}{7)}$ - √ $\frac{(-16}{7}$ )²

= √ (41.43 - (-2.29)²)

= √ (41.43-5.24)

= √ 36.19

standard deviation Ô = 6.02

Calculate the standard deviation.

Natural numbers are 40,39,32,29,25,26,32

Answer: 5.44

SOLUTION 1 :

Assumed Mean Method

Let us take A = 32 as assumed mean and form the following table.

x	d = x- 32	d²

25 26 29 32 32 39 40	-7 -6 -3 0 0 7 8	49 36 9 0 0 49 64
	∑d= -1	∑d² = 207

Here, n = 7

standard deviation Ô	=	√ ∑d²	-	√ (∑d)²
		√ n		√ n²

= √ $\frac{(207}{7)}$ - √ $\frac{(-1}{7}$ )²

= √ (29.57 - (-0.14)²)

= √ (29.57-0.02)

= √ 29.55

standard deviation Ô = 5.44

10)

Calculate the standard deviation.

Natural numbers are 43,37,35,29,20,26,35

Answer: 7.10

SOLUTION 1 :

Assumed Mean Method

Let us take A = 35 as assumed mean and form the following table.

x	d = x- 35	d²

20 26 29 35 35 37 43	-15 -9 -6 0 0 2 8	225 81 36 0 0 4 64
	∑d= -20	∑d² = 410

Here, n = 7

standard deviation Ô	=	√ ∑d²	-	√ (∑d)²
		√ n		√ n²

= √ $\frac{(410}{7)}$ - √ $\frac{(-20}{7}$ )²

= √ (58.57 - (-2.86)²)

= √ (58.57-8.18)

= √ 50.39

standard deviation Ô = 7.10