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 40,38,35,31,23,28,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 40,37,32,30,21,26,32

Answer:_______________

Calculate the standard deviation.

Natural numbers are 43,38,33,29,23,27,33

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,36,32,31,24,27,32

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,36,35,31,21,26,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,38,34,31,22,26,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,37,32,31,22,27,32

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,39,34,29,24,28,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 41,36,34,31,22,26,34

Answer:_______________

10)

Calculate the standard deviation.

Natural numbers are 42,38,32,29,25,28,32

Answer:_______________

Calculate the standard deviation.

Natural numbers are 40,38,35,31,23,28,35

Answer: 5.49

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 35	d²

23 28 31 35 35 38 40	-12 -7 -4 0 0 3 5	144 49 16 0 0 9 25
	∑d= -15	∑d² = 243

Here, n = 7

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

= √ $\frac{(243}{7)}$ - √ $\frac{(-15}{7}$ )²

= √ (34.71 - (-2.14)²)

= √ (34.71-4.58)

= √ 30.13

standard deviation Ô = 5.49

Calculate the standard deviation.

Natural numbers are 40,37,32,30,21,26,32

Answer: 5.91

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 32	d²

21 26 30 32 32 37 40	-11 -6 -2 0 0 5 8	121 36 4 0 0 25 64
	∑d= -6	∑d² = 250

Here, n = 7

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

= √ $\frac{(250}{7)}$ - √ $\frac{(-6}{7}$ )²

= √ (35.71 - (-0.86)²)

= √ (35.71-0.74)

= √ 34.97

standard deviation Ô = 5.91

Calculate the standard deviation.

Natural numbers are 43,38,33,29,23,27,33

Answer: 6.25

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 33	d²

23 27 29 33 33 38 43	-10 -6 -4 0 0 5 10	100 36 16 0 0 25 100
	∑d= -5	∑d² = 277

Here, n = 7

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

= √ $\frac{(277}{7)}$ - √ $\frac{(-5}{7}$ )²

= √ (39.57 - (-0.71)²)

= √ (39.57-0.50)

= √ 39.07

standard deviation Ô = 6.25

Calculate the standard deviation.

Natural numbers are 44,36,32,31,24,27,32

Answer: 5.97

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 36 44	-8 -5 -1 0 0 4 12	64 25 1 0 0 16 144
	∑d= 2	∑d² = 250

Here, n = 7

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

= √ $\frac{(250}{7)}$ - √ $\frac{(2}{7}$ )²

= √ (35.71 - (0.29)²)

= √ (35.71-0.08)

= √ 35.63

standard deviation Ô = 5.97

Calculate the standard deviation.

Natural numbers are 44,36,35,31,21,26,35

Answer: 6.90

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 31 35 35 36 44	-14 -9 -4 0 0 1 9	196 81 16 0 0 1 81
	∑d= -17	∑d² = 375

Here, n = 7

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

= √ $\frac{(375}{7)}$ - √ $\frac{(-17}{7}$ )²

= √ (53.57 - (-2.43)²)

= √ (53.57-5.90)

= √ 47.67

standard deviation Ô = 6.90

Calculate the standard deviation.

Natural numbers are 44,38,34,31,22,26,34

Answer: 6.78

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

22 26 31 34 34 38 44	-12 -8 -3 0 0 4 10	144 64 9 0 0 16 100
	∑d= -9	∑d² = 333

Here, n = 7

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

= √ $\frac{(333}{7)}$ - √ $\frac{(-9}{7}$ )²

= √ (47.57 - (-1.29)²)

= √ (47.57-1.66)

= √ 45.91

standard deviation Ô = 6.78

Calculate the standard deviation.

Natural numbers are 44,37,32,31,22,27,32

Answer: 6.49

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 32	d²

22 27 31 32 32 37 44	-10 -5 -1 0 0 5 12	100 25 1 0 0 25 144
	∑d= 1	∑d² = 295

Here, n = 7

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

= √ $\frac{(295}{7)}$ - √ $\frac{(1}{7}$ )²

= √ (42.14 - (0.14)²)

= √ (42.14-0.02)

= √ 42.12

standard deviation Ô = 6.49

Calculate the standard deviation.

Natural numbers are 44,39,34,29,24,28,34

Answer: 6.33

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

24 28 29 34 34 39 44	-10 -6 -5 0 0 5 10	100 36 25 0 0 25 100
	∑d= -6	∑d² = 286

Here, n = 7

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

= √ $\frac{(286}{7)}$ - √ $\frac{(-6}{7}$ )²

= √ (40.86 - (-0.86)²)

= √ (40.86-0.74)

= √ 40.12

standard deviation Ô = 6.33

Calculate the standard deviation.

Natural numbers are 41,36,34,31,22,26,34

Answer: 5.88

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

22 26 31 34 34 36 41	-12 -8 -3 0 0 2 7	144 64 9 0 0 4 49
	∑d= -14	∑d² = 270

Here, n = 7

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

= √ $\frac{(270}{7)}$ - √ $\frac{(-14}{7}$ )²

= √ (38.57 - (-2.00)²)

= √ (38.57-4.00)

= √ 34.57

standard deviation Ô = 5.88

10)

Calculate the standard deviation.

Natural numbers are 42,38,32,29,25,28,32

Answer: 5.47

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 32	d²

25 28 29 32 32 38 42	-7 -4 -3 0 0 6 10	49 16 9 0 0 36 100
	∑d= 2	∑d² = 210

Here, n = 7

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

= √ $\frac{(210}{7)}$ - √ $\frac{(2}{7}$ )²

= √ (30.00 - (0.29)²)

= √ (30.00-0.08)

= √ 29.92

standard deviation Ô = 5.47