Sasi Math (Revised for 1024)

Scroll:statistics >> standard deviation >> saq (4246)

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 stadard deviation.

Natural numbers are 10,21,15,9,3,4

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 14,20,16,8,3,4

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 14,22,15,8,2,6

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 12,20,17,7,3,5

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 11,21,16,7,3,6

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 13,20,15,9,3,6

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 12,22,17,8,3,5

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 14,20,17,8,3,5

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 14,20,15,8,3,4

Answer:_______________

10)

Calculate the stadard deviation.

Natural numbers are 14,22,17,7,3,5

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 10,21,15,9,3,4

Answer: 6.21

SOLUTION 1 :

Direct Method

x	= x²

3 4 9 15 21 10	9 16 81 225 441 100
∑x = 62	∑x²= 872

Here, n = 6

standard deviation Ô		=	√ ∑x²	-	√ (∑x)²
			√ n		√ n²

= √ $\frac{872}{6}$ - √ $\frac{(62}{6}$ )²

= √ (145.33 - 10.332)

= √ (145.33-106.71)

= √ 38.62

standard deviation Ô = 6.21

Calculate the stadard deviation.

Natural numbers are 14,20,16,8,3,4

Answer: 6.29

SOLUTION 1 :

Direct Method

x	= x²

3 4 8 16 20 14	9 16 64 256 400 196
∑x = 65	∑x²= 941

Here, n = 6

standard deviation Ô		=	√ ∑x²	-	√ (∑x)²
			√ n		√ n²

= √ $\frac{941}{6}$ - √ $\frac{(65}{6}$ )²

= √ (156.83 - 10.832)

= √ (156.83-117.29)

= √ 39.54

standard deviation Ô = 6.29

Calculate the stadard deviation.

Natural numbers are 14,22,15,8,2,6

Answer: 6.59

SOLUTION 1 :

Direct Method

x	= x²

2 6 8 15 22 14	4 36 64 225 484 196
∑x = 67	∑x²= 1009

Here, n = 6

standard deviation Ô		=	√ ∑x²	-	√ (∑x)²
			√ n		√ n²

= √ $\frac{1009}{6}$ - √ $\frac{(67}{6}$ )²

= √ (168.17 - 11.172)

= √ (168.17-124.77)

= √ 43.40

standard deviation Ô = 6.59

Calculate the stadard deviation.

Natural numbers are 12,20,17,7,3,5

Answer: 6.23

SOLUTION 1 :

Direct Method

x	= x²

3 5 7 17 20 12	9 25 49 289 400 144
∑x = 64	∑x²= 916

Here, n = 6

standard deviation Ô		=	√ ∑x²	-	√ (∑x)²
			√ n		√ n²

= √ $\frac{916}{6}$ - √ $\frac{(64}{6}$ )²

= √ (152.67 - 10.672)

= √ (152.67-113.85)

= √ 38.82

standard deviation Ô = 6.23

Calculate the stadard deviation.

Natural numbers are 11,21,16,7,3,6

Answer: 6.18

SOLUTION 1 :

Direct Method

x	= x²

3 6 7 16 21 11	9 36 49 256 441 121
∑x = 64	∑x²= 912

Here, n = 6

standard deviation Ô		=	√ ∑x²	-	√ (∑x)²
			√ n		√ n²

= √ $\frac{912}{6}$ - √ $\frac{(64}{6}$ )²

= √ (152.00 - 10.672)

= √ (152.00-113.85)

= √ 38.15

standard deviation Ô = 6.18

Calculate the stadard deviation.

Natural numbers are 13,20,15,9,3,6

Answer: 5.69

SOLUTION 1 :

Direct Method

x	= x²

3 6 9 15 20 13	9 36 81 225 400 169
∑x = 66	∑x²= 920

Here, n = 6

standard deviation Ô		=	√ ∑x²	-	√ (∑x)²
			√ n		√ n²

= √ $\frac{920}{6}$ - √ $\frac{(66}{6}$ )²

= √ (153.33 - 11.002)

= √ (153.33-121.00)

= √ 32.33

standard deviation Ô = 5.69

Calculate the stadard deviation.

Natural numbers are 12,22,17,8,3,5

Answer: 6.66

SOLUTION 1 :

Direct Method

x	= x²

3 5 8 17 22 12	9 25 64 289 484 144
∑x = 67	∑x²= 1015

Here, n = 6

standard deviation Ô		=	√ ∑x²	-	√ (∑x)²
			√ n		√ n²

= √ $\frac{1015}{6}$ - √ $\frac{(67}{6}$ )²

= √ (169.17 - 11.172)

= √ (169.17-124.77)

= √ 44.40

standard deviation Ô = 6.66

Calculate the stadard deviation.

Natural numbers are 14,20,17,8,3,5

Answer: 6.25

SOLUTION 1 :

Direct Method

x	= x²

3 5 8 17 20 14	9 25 64 289 400 196
∑x = 67	∑x²= 983

Here, n = 6

standard deviation Ô		=	√ ∑x²	-	√ (∑x)²
			√ n		√ n²

= √ $\frac{983}{6}$ - √ $\frac{(67}{6}$ )²

= √ (163.83 - 11.172)

= √ (163.83-124.77)

= √ 39.06

standard deviation Ô = 6.25

Calculate the stadard deviation.

Natural numbers are 14,20,15,8,3,4

Answer: 6.15

SOLUTION 1 :

Direct Method

x	= x²

3 4 8 15 20 14	9 16 64 225 400 196
∑x = 64	∑x²= 910

Here, n = 6

standard deviation Ô		=	√ ∑x²	-	√ (∑x)²
			√ n		√ n²

= √ $\frac{910}{6}$ - √ $\frac{(64}{6}$ )²

= √ (151.67 - 10.672)

= √ (151.67-113.85)

= √ 37.82

standard deviation Ô = 6.15

10)

Calculate the stadard deviation.

Natural numbers are 14,22,17,7,3,5

Answer: 6.85

SOLUTION 1 :

Direct Method

x	= x²

3 5 7 17 22 14	9 25 49 289 484 196
∑x = 68	∑x²= 1052

Here, n = 6

standard deviation Ô		=	√ ∑x²	-	√ (∑x)²
			√ n		√ n²

= √ $\frac{1052}{6}$ - √ $\frac{(68}{6}$ )²

= √ (175.33 - 11.332)

= √ (175.33-128.37)

= √ 46.96

standard deviation Ô = 6.85