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 10,22,16,8,3,4

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 14,21,17,7,2,5

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 13,21,16,9,3,6

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 11,21,17,8,3,6

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 11,22,15,9,2,4

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 14,22,15,7,2,4

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 11,22,15,8,2,4

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 14,20,17,8,2,5

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 12,22,15,9,2,4

Answer:_______________

10)

Calculate the stadard deviation.

Natural numbers are 13,21,17,9,3,4

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 10,22,16,8,3,4

Answer: 6.68

SOLUTION 1 :

Direct Method

x	= x²

3 4 8 16 22 10	9 16 64 256 484 100
∑x = 63	∑x²= 929

Here, n = 6

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

= √ $\frac{929}{6}$ - √ $\frac{(63}{6}$ )²

= √ (154.83 - 10.502)

= √ (154.83-110.25)

= √ 44.58

standard deviation Ô = 6.68

Calculate the stadard deviation.

Natural numbers are 14,21,17,7,2,5

Answer: 6.81

SOLUTION 1 :

Direct Method

x	= x²

2 5 7 17 21 14	4 25 49 289 441 196
∑x = 66	∑x²= 1004

Here, n = 6

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

= √ $\frac{1004}{6}$ - √ $\frac{(66}{6}$ )²

= √ (167.33 - 11.002)

= √ (167.33-121.00)

= √ 46.33

standard deviation Ô = 6.81

Calculate the stadard deviation.

Natural numbers are 13,21,16,9,3,6

Answer: 6.08

SOLUTION 1 :

Direct Method

x	= x²

3 6 9 16 21 13	9 36 81 256 441 169
∑x = 68	∑x²= 992

Here, n = 6

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

= √ $\frac{992}{6}$ - √ $\frac{(68}{6}$ )²

= √ (165.33 - 11.332)

= √ (165.33-128.37)

= √ 36.96

standard deviation Ô = 6.08

Calculate the stadard deviation.

Natural numbers are 11,21,17,8,3,6

Answer: 6.24

SOLUTION 1 :

Direct Method

x	= x²

3 6 8 17 21 11	9 36 64 289 441 121
∑x = 66	∑x²= 960

Here, n = 6

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

= √ $\frac{960}{6}$ - √ $\frac{(66}{6}$ )²

= √ (160.00 - 11.002)

= √ (160.00-121.00)

= √ 39.00

standard deviation Ô = 6.24

Calculate the stadard deviation.

Natural numbers are 11,22,15,9,2,4

Answer: 6.70

SOLUTION 1 :

Direct Method

x	= x²

2 4 9 15 22 11	4 16 81 225 484 121
∑x = 63	∑x²= 931

Here, n = 6

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

= √ $\frac{931}{6}$ - √ $\frac{(63}{6}$ )²

= √ (155.17 - 10.502)

= √ (155.17-110.25)

= √ 44.92

standard deviation Ô = 6.70

Calculate the stadard deviation.

Natural numbers are 14,22,15,7,2,4

Answer: 6.96

SOLUTION 1 :

Direct Method

x	= x²

2 4 7 15 22 14	4 16 49 225 484 196
∑x = 64	∑x²= 974

Here, n = 6

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

= √ $\frac{974}{6}$ - √ $\frac{(64}{6}$ )²

= √ (162.33 - 10.672)

= √ (162.33-113.85)

= √ 48.48

standard deviation Ô = 6.96

Calculate the stadard deviation.

Natural numbers are 11,22,15,8,2,4

Answer: 6.75

SOLUTION 1 :

Direct Method

x	= x²

2 4 8 15 22 11	4 16 64 225 484 121
∑x = 62	∑x²= 914

Here, n = 6

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

= √ $\frac{914}{6}$ - √ $\frac{(62}{6}$ )²

= √ (152.33 - 10.332)

= √ (152.33-106.71)

= √ 45.62

standard deviation Ô = 6.75

Calculate the stadard deviation.

Natural numbers are 14,20,17,8,2,5

Answer: 6.48

SOLUTION 1 :

Direct Method

x	= x²

2 5 8 17 20 14	4 25 64 289 400 196
∑x = 66	∑x²= 978

Here, n = 6

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

= √ $\frac{978}{6}$ - √ $\frac{(66}{6}$ )²

= √ (163.00 - 11.002)

= √ (163.00-121.00)

= √ 42.00

standard deviation Ô = 6.48

Calculate the stadard deviation.

Natural numbers are 12,22,15,9,2,4

Answer: 6.72

SOLUTION 1 :

Direct Method

x	= x²

2 4 9 15 22 12	4 16 81 225 484 144
∑x = 64	∑x²= 954

Here, n = 6

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

= √ $\frac{954}{6}$ - √ $\frac{(64}{6}$ )²

= √ (159.00 - 10.672)

= √ (159.00-113.85)

= √ 45.15

standard deviation Ô = 6.72

10)

Calculate the stadard deviation.

Natural numbers are 13,21,17,9,3,4

Answer: 6.54

SOLUTION 1 :

Direct Method

x	= x²

3 4 9 17 21 13	9 16 81 289 441 169
∑x = 67	∑x²= 1005

Here, n = 6

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

= √ $\frac{1005}{6}$ - √ $\frac{(67}{6}$ )²

= √ (167.50 - 11.172)

= √ (167.50-124.77)

= √ 42.73

standard deviation Ô = 6.54