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 10,22,16,8,3,5

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 10,22,15,7,3,6

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 14,20,15,9,3,5

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 12,22,16,9,3,5

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 11,22,17,7,3,6

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 13,20,15,7,2,4

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 10,18,15,8,2,6

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 12,19,17,8,3,4

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 10,21,17,8,2,4

Answer:_______________

10)

Calculate the stadard deviation.

Natural numbers are 14,19,15,8,3,4

Answer:_______________

Calculate the stadard deviation.

Natural numbers are 10,22,16,8,3,5

Answer: 6.52

SOLUTION 1 :

Direct Method

x	= x²

3 5 8 16 22 10	9 25 64 256 484 100
∑x = 64	∑x²= 938

Here, n = 6

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

= √ $\frac{938}{6}$ - √ $\frac{(64}{6}$ )²

= √ (156.33 - 10.672)

= √ (156.33-113.85)

= √ 42.48

standard deviation Ô = 6.52

Calculate the stadard deviation.

Natural numbers are 10,22,15,7,3,6

Answer: 6.34

SOLUTION 1 :

Direct Method

x	= x²

3 6 7 15 22 10	9 36 49 225 484 100
∑x = 63	∑x²= 903

Here, n = 6

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

= √ $\frac{903}{6}$ - √ $\frac{(63}{6}$ )²

= √ (150.50 - 10.502)

= √ (150.50-110.25)

= √ 40.25

standard deviation Ô = 6.34

Calculate the stadard deviation.

Natural numbers are 14,20,15,9,3,5

Answer: 5.92

SOLUTION 1 :

Direct Method

x	= x²

3 5 9 15 20 14	9 25 81 225 400 196
∑x = 66	∑x²= 936

Here, n = 6

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

= √ $\frac{936}{6}$ - √ $\frac{(66}{6}$ )²

= √ (156.00 - 11.002)

= √ (156.00-121.00)

= √ 35.00

standard deviation Ô = 5.92

Calculate the stadard deviation.

Natural numbers are 12,22,16,9,3,5

Answer: 6.46

SOLUTION 1 :

Direct Method

x	= x²

3 5 9 16 22 12	9 25 81 256 484 144
∑x = 67	∑x²= 999

Here, n = 6

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

= √ $\frac{999}{6}$ - √ $\frac{(67}{6}$ )²

= √ (166.50 - 11.172)

= √ (166.50-124.77)

= √ 41.73

standard deviation Ô = 6.46

Calculate the stadard deviation.

Natural numbers are 11,22,17,7,3,6

Answer: 6.61

SOLUTION 1 :

Direct Method

x	= x²

3 6 7 17 22 11	9 36 49 289 484 121
∑x = 66	∑x²= 988

Here, n = 6

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

= √ $\frac{988}{6}$ - √ $\frac{(66}{6}$ )²

= √ (164.67 - 11.002)

= √ (164.67-121.00)

= √ 43.67

standard deviation Ô = 6.61

Calculate the stadard deviation.

Natural numbers are 13,20,15,7,2,4

Answer: 6.36

SOLUTION 1 :

Direct Method

x	= x²

2 4 7 15 20 13	4 16 49 225 400 169
∑x = 61	∑x²= 863

Here, n = 6

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

= √ $\frac{863}{6}$ - √ $\frac{(61}{6}$ )²

= √ (143.83 - 10.172)

= √ (143.83-103.43)

= √ 40.40

standard deviation Ô = 6.36

Calculate the stadard deviation.

Natural numbers are 10,18,15,8,2,6

Answer: 5.37

SOLUTION 1 :

Direct Method

x	= x²

2 6 8 15 18 10	4 36 64 225 324 100
∑x = 59	∑x²= 753

Here, n = 6

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

= √ $\frac{753}{6}$ - √ $\frac{(59}{6}$ )²

= √ (125.50 - 9.832)

= √ (125.50-96.63)

= √ 28.87

standard deviation Ô = 5.37

Calculate the stadard deviation.

Natural numbers are 12,19,17,8,3,4

Answer: 6.08

SOLUTION 1 :

Direct Method

x	= x²

3 4 8 17 19 12	9 16 64 289 361 144
∑x = 63	∑x²= 883

Here, n = 6

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

= √ $\frac{883}{6}$ - √ $\frac{(63}{6}$ )²

= √ (147.17 - 10.502)

= √ (147.17-110.25)

= √ 36.92

standard deviation Ô = 6.08

Calculate the stadard deviation.

Natural numbers are 10,21,17,8,2,4

Answer: 6.75

SOLUTION 1 :

Direct Method

x	= x²

2 4 8 17 21 10	4 16 64 289 441 100
∑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

10)

Calculate the stadard deviation.

Natural numbers are 14,19,15,8,3,4

Answer: 5.91

SOLUTION 1 :

Direct Method

x	= x²

3 4 8 15 19 14	9 16 64 225 361 196
∑x = 63	∑x²= 871

Here, n = 6

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

= √ $\frac{871}{6}$ - √ $\frac{(63}{6}$ )²

= √ (145.17 - 10.502)

= √ (145.17-110.25)

= √ 34.92

standard deviation Ô = 5.91