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 44,36,34,29,20,26,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,39,34,31,21,26,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 42,36,34,29,25,28,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 42,38,35,31,20,26,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 42,38,34,30,20,28,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 41,38,33,30,23,27,33

Answer:_______________

Calculate the standard deviation.

Natural numbers are 41,38,34,30,25,28,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 42,38,35,31,20,27,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 40,39,32,31,24,28,32

Answer:_______________

10)

Calculate the standard deviation.

Natural numbers are 42,39,34,31,21,27,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,36,34,29,20,26,34

Answer: 7.14

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 29 34 34 36 44	-14 -8 -5 0 0 2 10	196 64 25 0 0 4 100
	∑d= -15	∑d² = 389

Here, n = 7

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

= √ $\frac{(389}{7)}$ - √ $\frac{(-15}{7}$ )²

= √ (55.57 - (-2.14)²)

= √ (55.57-4.58)

= √ 50.99

standard deviation Ô = 7.14

Calculate the standard deviation.

Natural numbers are 44,39,34,31,21,26,34

Answer: 7.13

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

21 26 31 34 34 39 44	-13 -8 -3 0 0 5 10	169 64 9 0 0 25 100
	∑d= -9	∑d² = 367

Here, n = 7

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

= √ $\frac{(367}{7)}$ - √ $\frac{(-9}{7}$ )²

= √ (52.43 - (-1.29)²)

= √ (52.43-1.66)

= √ 50.77

standard deviation Ô = 7.13

Calculate the standard deviation.

Natural numbers are 42,36,34,29,25,28,34

Answer: 5.29

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

25 28 29 34 34 36 42	-9 -6 -5 0 0 2 8	81 36 25 0 0 4 64
	∑d= -10	∑d² = 210

Here, n = 7

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

= √ $\frac{(210}{7)}$ - √ $\frac{(-10}{7}$ )²

= √ (30.00 - (-1.43)²)

= √ (30.00-2.04)

= √ 27.96

standard deviation Ô = 5.29

Calculate the standard deviation.

Natural numbers are 42,38,35,31,20,26,35

Answer: 6.91

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 31 35 35 38 42	-15 -9 -4 0 0 3 7	225 81 16 0 0 9 49
	∑d= -18	∑d² = 380

Here, n = 7

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

= √ $\frac{(380}{7)}$ - √ $\frac{(-18}{7}$ )²

= √ (54.29 - (-2.57)²)

= √ (54.29-6.60)

= √ 47.69

standard deviation Ô = 6.91

Calculate the standard deviation.

Natural numbers are 42,38,34,30,20,28,34

Answer: 6.63

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

20 28 30 34 34 38 42	-14 -6 -4 0 0 4 8	196 36 16 0 0 16 64
	∑d= -12	∑d² = 328

Here, n = 7

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

= √ $\frac{(328}{7)}$ - √ $\frac{(-12}{7}$ )²

= √ (46.86 - (-1.71)²)

= √ (46.86-2.92)

= √ 43.94

standard deviation Ô = 6.63

Calculate the standard deviation.

Natural numbers are 41,38,33,30,23,27,33

Answer: 5.72

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 30 33 33 38 41	-10 -6 -3 0 0 5 8	100 36 9 0 0 25 64
	∑d= -6	∑d² = 234

Here, n = 7

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

= √ $\frac{(234}{7)}$ - √ $\frac{(-6}{7}$ )²

= √ (33.43 - (-0.86)²)

= √ (33.43-0.74)

= √ 32.69

standard deviation Ô = 5.72

Calculate the standard deviation.

Natural numbers are 41,38,34,30,25,28,34

Answer: 5.20

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

25 28 30 34 34 38 41	-9 -6 -4 0 0 4 7	81 36 16 0 0 16 49
	∑d= -8	∑d² = 198

Here, n = 7

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

= √ $\frac{(198}{7)}$ - √ $\frac{(-8}{7}$ )²

= √ (28.29 - (-1.14)²)

= √ (28.29-1.30)

= √ 26.99

standard deviation Ô = 5.20

Calculate the standard deviation.

Natural numbers are 42,38,35,31,20,27,35

Answer: 6.78

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 35	d²

20 27 31 35 35 38 42	-15 -8 -4 0 0 3 7	225 64 16 0 0 9 49
	∑d= -17	∑d² = 363

Here, n = 7

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

= √ $\frac{(363}{7)}$ - √ $\frac{(-17}{7}$ )²

= √ (51.86 - (-2.43)²)

= √ (51.86-5.90)

= √ 45.96

standard deviation Ô = 6.78

Calculate the standard deviation.

Natural numbers are 40,39,32,31,24,28,32

Answer: 5.26

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 32	d²

24 28 31 32 32 39 40	-8 -4 -1 0 0 7 8	64 16 1 0 0 49 64
	∑d= 2	∑d² = 194

Here, n = 7

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

= √ $\frac{(194}{7)}$ - √ $\frac{(2}{7}$ )²

= √ (27.71 - (0.29)²)

= √ (27.71-0.08)

= √ 27.63

standard deviation Ô = 5.26

10)

Calculate the standard deviation.

Natural numbers are 42,39,34,31,21,27,34

Answer: 6.57

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

21 27 31 34 34 39 42	-13 -7 -3 0 0 5 8	169 49 9 0 0 25 64
	∑d= -10	∑d² = 316

Here, n = 7

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

= √ $\frac{(316}{7)}$ - √ $\frac{(-10}{7}$ )²

= √ (45.14 - (-1.43)²)

= √ (45.14-2.04)

= √ 43.10

standard deviation Ô = 6.57