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 42,36,33,29,21,26,33

Answer:_______________

Calculate the standard deviation.

Natural numbers are 43,39,32,31,24,27,32

Answer:_______________

Calculate the standard deviation.

Natural numbers are 43,37,34,29,24,26,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 41,37,35,29,24,26,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 42,38,32,31,25,26,32

Answer:_______________

Calculate the standard deviation.

Natural numbers are 40,37,35,29,21,26,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 41,36,35,30,25,26,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,38,35,31,20,28,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 41,36,33,31,22,26,33

Answer:_______________

10)

Calculate the standard deviation.

Natural numbers are 44,36,35,29,23,27,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 42,36,33,29,21,26,33

Answer: 6.34

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 33	d²

21 26 29 33 33 36 42	-12 -7 -4 0 0 3 9	144 49 16 0 0 9 81
	∑d= -11	∑d² = 299

Here, n = 7

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

= √ $\frac{(299}{7)}$ - √ $\frac{(-11}{7}$ )²

= √ (42.71 - (-1.57)²)

= √ (42.71-2.46)

= √ 40.25

standard deviation Ô = 6.34

Calculate the standard deviation.

Natural numbers are 43,39,32,31,24,27,32

Answer: 6.07

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 31 32 32 39 43	-8 -5 -1 0 0 7 11	64 25 1 0 0 49 121
	∑d= 4	∑d² = 260

Here, n = 7

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

= √ $\frac{(260}{7)}$ - √ $\frac{(4}{7}$ )²

= √ (37.14 - (0.57)²)

= √ (37.14-0.32)

= √ 36.82

standard deviation Ô = 6.07

Calculate the standard deviation.

Natural numbers are 43,37,34,29,24,26,34

Answer: 6.12

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

24 26 29 34 34 37 43	-10 -8 -5 0 0 3 9	100 64 25 0 0 9 81
	∑d= -11	∑d² = 279

Here, n = 7

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

= √ $\frac{(279}{7)}$ - √ $\frac{(-11}{7}$ )²

= √ (39.86 - (-1.57)²)

= √ (39.86-2.46)

= √ 37.40

standard deviation Ô = 6.12

Calculate the standard deviation.

Natural numbers are 41,37,35,29,24,26,35

Answer: 5.75

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 37 41	-11 -9 -6 0 0 2 6	121 81 36 0 0 4 36
	∑d= -18	∑d² = 278

Here, n = 7

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

= √ $\frac{(278}{7)}$ - √ $\frac{(-18}{7}$ )²

= √ (39.71 - (-2.57)²)

= √ (39.71-6.60)

= √ 33.11

standard deviation Ô = 5.75

Calculate the standard deviation.

Natural numbers are 42,38,32,31,25,26,32

Answer: 5.62

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 31 32 32 38 42	-7 -6 -1 0 0 6 10	49 36 1 0 0 36 100
	∑d= 2	∑d² = 222

Here, n = 7

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

= √ $\frac{(222}{7)}$ - √ $\frac{(2}{7}$ )²

= √ (31.71 - (0.29)²)

= √ (31.71-0.08)

= √ 31.63

standard deviation Ô = 5.62

Calculate the standard deviation.

Natural numbers are 40,37,35,29,21,26,35

Answer: 6.24

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 35	d²

21 26 29 35 35 37 40	-14 -9 -6 0 0 2 5	196 81 36 0 0 4 25
	∑d= -22	∑d² = 342

Here, n = 7

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

= √ $\frac{(342}{7)}$ - √ $\frac{(-22}{7}$ )²

= √ (48.86 - (-3.14)²)

= √ (48.86-9.86)

= √ 39.00

standard deviation Ô = 6.24

Calculate the standard deviation.

Natural numbers are 41,36,35,30,25,26,35

Answer: 5.37

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 30 35 35 36 41	-10 -9 -5 0 0 1 6	100 81 25 0 0 1 36
	∑d= -17	∑d² = 243

Here, n = 7

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

= √ $\frac{(243}{7)}$ - √ $\frac{(-17}{7}$ )²

= √ (34.71 - (-2.43)²)

= √ (34.71-5.90)

= √ 28.81

standard deviation Ô = 5.37

Calculate the standard deviation.

Natural numbers are 44,38,35,31,20,28,35

Answer: 7.09

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 35	d²

20 28 31 35 35 38 44	-15 -7 -4 0 0 3 9	225 49 16 0 0 9 81
	∑d= -14	∑d² = 380

Here, n = 7

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

= √ $\frac{(380}{7)}$ - √ $\frac{(-14}{7}$ )²

= √ (54.29 - (-2.00)²)

= √ (54.29-4.00)

= √ 50.29

standard deviation Ô = 7.09

Calculate the standard deviation.

Natural numbers are 41,36,33,31,22,26,33

Answer: 5.80

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 33	d²

22 26 31 33 33 36 41	-11 -7 -2 0 0 3 8	121 49 4 0 0 9 64
	∑d= -9	∑d² = 247

Here, n = 7

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

= √ $\frac{(247}{7)}$ - √ $\frac{(-9}{7}$ )²

= √ (35.29 - (-1.29)²)

= √ (35.29-1.66)

= √ 33.63

standard deviation Ô = 5.80

10)

Calculate the standard deviation.

Natural numbers are 44,36,35,29,23,27,35

Answer: 6.43

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 35	d²

23 27 29 35 35 36 44	-12 -8 -6 0 0 1 9	144 64 36 0 0 1 81
	∑d= -16	∑d² = 326

Here, n = 7

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

= √ $\frac{(326}{7)}$ - √ $\frac{(-16}{7}$ )²

= √ (46.57 - (-2.29)²)

= √ (46.57-5.24)

= √ 41.33

standard deviation Ô = 6.43