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 44,36,34,30,23,26,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 40,39,33,29,20,28,33

Answer:_______________

Calculate the standard deviation.

Natural numbers are 42,38,34,29,22,28,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 42,39,33,31,20,26,33

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,39,35,31,21,28,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 40,38,32,30,24,27,32

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,37,35,29,21,28,35

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,36,34,31,24,27,34

Answer:_______________

Calculate the standard deviation.

Natural numbers are 41,38,34,29,25,27,34

Answer:_______________

10)

Calculate the standard deviation.

Natural numbers are 40,36,32,29,24,28,32

Answer:_______________

Calculate the standard deviation.

Natural numbers are 44,36,34,30,23,26,34

Answer: 6.41

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

23 26 30 34 34 36 44	-11 -8 -4 0 0 2 10	121 64 16 0 0 4 100
	∑d= -11	∑d² = 305

Here, n = 7

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

= √ $\frac{(305}{7)}$ - √ $\frac{(-11}{7}$ )²

= √ (43.57 - (-1.57)²)

= √ (43.57-2.46)

= √ 41.11

standard deviation Ô = 6.41

Calculate the standard deviation.

Natural numbers are 40,39,33,29,20,28,33

Answer: 6.36

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 33	d²

20 28 29 33 33 39 40	-13 -5 -4 0 0 6 7	169 25 16 0 0 36 49
	∑d= -9	∑d² = 295

Here, n = 7

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

= √ $\frac{(295}{7)}$ - √ $\frac{(-9}{7}$ )²

= √ (42.14 - (-1.29)²)

= √ (42.14-1.66)

= √ 40.48

standard deviation Ô = 6.36

Calculate the standard deviation.

Natural numbers are 42,38,34,29,22,28,34

Answer: 6.18

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

22 28 29 34 34 38 42	-12 -6 -5 0 0 4 8	144 36 25 0 0 16 64
	∑d= -11	∑d² = 285

Here, n = 7

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

= √ $\frac{(285}{7)}$ - √ $\frac{(-11}{7}$ )²

= √ (40.71 - (-1.57)²)

= √ (40.71-2.46)

= √ 38.25

standard deviation Ô = 6.18

Calculate the standard deviation.

Natural numbers are 42,39,33,31,20,26,33

Answer: 6.89

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 33	d²

20 26 31 33 33 39 42	-13 -7 -2 0 0 6 9	169 49 4 0 0 36 81
	∑d= -7	∑d² = 339

Here, n = 7

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

= √ $\frac{(339}{7)}$ - √ $\frac{(-7}{7}$ )²

= √ (48.43 - (-1.00)²)

= √ (48.43-1.00)

= √ 47.43

standard deviation Ô = 6.89

Calculate the standard deviation.

Natural numbers are 44,39,35,31,21,28,35

Answer: 6.94

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 35	d²

21 28 31 35 35 39 44	-14 -7 -4 0 0 4 9	196 49 16 0 0 16 81
	∑d= -12	∑d² = 358

Here, n = 7

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

= √ $\frac{(358}{7)}$ - √ $\frac{(-12}{7}$ )²

= √ (51.14 - (-1.71)²)

= √ (51.14-2.92)

= √ 48.22

standard deviation Ô = 6.94

Calculate the standard deviation.

Natural numbers are 40,38,32,30,24,27,32

Answer: 5.25

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 30 32 32 38 40	-8 -5 -2 0 0 6 8	64 25 4 0 0 36 64
	∑d= -1	∑d² = 193

Here, n = 7

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

= √ $\frac{(193}{7)}$ - √ $\frac{(-1}{7}$ )²

= √ (27.57 - (-0.14)²)

= √ (27.57-0.02)

= √ 27.55

standard deviation Ô = 5.25

Calculate the standard deviation.

Natural numbers are 44,37,35,29,21,28,35

Answer: 6.86

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 35	d²

21 28 29 35 35 37 44	-14 -7 -6 0 0 2 9	196 49 36 0 0 4 81
	∑d= -16	∑d² = 366

Here, n = 7

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

= √ $\frac{(366}{7)}$ - √ $\frac{(-16}{7}$ )²

= √ (52.29 - (-2.29)²)

= √ (52.29-5.24)

= √ 47.05

standard deviation Ô = 6.86

Calculate the standard deviation.

Natural numbers are 44,36,34,31,24,27,34

Answer: 6.01

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

24 27 31 34 34 36 44	-10 -7 -3 0 0 2 10	100 49 9 0 0 4 100
	∑d= -8	∑d² = 262

Here, n = 7

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

= √ $\frac{(262}{7)}$ - √ $\frac{(-8}{7}$ )²

= √ (37.43 - (-1.14)²)

= √ (37.43-1.30)

= √ 36.13

standard deviation Ô = 6.01

Calculate the standard deviation.

Natural numbers are 41,38,34,29,25,27,34

Answer: 5.42

SOLUTION 1 :

Assumed Mean Method

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

x	d = x- 34	d²

25 27 29 34 34 38 41	-9 -7 -5 0 0 4 7	81 49 25 0 0 16 49
	∑d= -10	∑d² = 220

Here, n = 7

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

= √ $\frac{(220}{7)}$ - √ $\frac{(-10}{7}$ )²

= √ (31.43 - (-1.43)²)

= √ (31.43-2.04)

= √ 29.39

standard deviation Ô = 5.42

10)

Calculate the standard deviation.

Natural numbers are 40,36,32,29,24,28,32

Answer: 4.89

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 29 32 32 36 40	-8 -4 -3 0 0 4 8	64 16 9 0 0 16 64
	∑d= -3	∑d² = 169

Here, n = 7

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

= √ $\frac{(169}{7)}$ - √ $\frac{(-3}{7}$ )²

= √ (24.14 - (-0.43)²)

= √ (24.14-0.18)

= √ 23.96

standard deviation Ô = 4.89