10th Grade Statistics Solution3

In this page 10th grade statistics solution3 we are going to see solution of some practice questions of 10th grade statistics worksheet1.

Question 7 :

Calculate the standard deviation of the following data

     x     3     8    13    18    23

          7    10    15    10    8

Solution:

Since these are grouped data we don't have to write them as ascending order.

Let us use actual mean method to find standard deviation.


x



f



d = x - 13





fd²


3

7

3 - 13 = -10

100

700

8

10

8 - 13 = -5

25

250

13

15

13 - 13 = 0

0

0

18

10

18 - 13 = 5

25

250

23

8

23 - 13 = 10

100

800

Σ f = 50

Σfd²=2000

 σ  = √(Σfd²/Σf)

        =  √(2000/50)

        = √40

        = 6.32455

        = 6.32


Question 8 :

The number of books bought at a book fair 200 students from a school are given in the following table.

Number of books           0       1        2       3        4

Number of students       35     64       68     18       15

calculate the standard deviation.

Solution:


x



f



d = x - 2





fd²


0

35

0 - 2 = -2

4

140

1

64

1 - 2 = -1

1

64

2

68

2 - 2 = 0

0

0

3

18

3 - 2 = 1

1

18

4

15

4 - 2 = 2

4

60

Σ f = 200

Σfd²=282

 σ  = √(Σfd²/Σf)

        =  √(282/200)

        = √1.41

        = 1.18


10th grade statistics solution3 10th grade statistics solution3

Question 9:

Calculate the variance of the following table.

x    2    4    6     8    10    12    14    16

f    4    4    5    15     8      5      4    5

Solution:


x



f



d = x - 8





fd²


2

4

2 - 8 = -6

36

144

4

4

4 - 8 = -4

16

64

6

5

6 - 8 = -2

4

20

8

15

8 - 8 = 0

0

0

10

8

10 - 8 = 2

4

32

12

5

12 - 8 = 4

16

80

14

4

14 - 8 = 6

36

144

16

5

16 - 8 = 8

64

 320

Σ f = 50

Σfd²=804

 σ²  = √(Σfd²/Σf)

        =  √(804/50)

        = 16.08


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