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Introduction - Sample data sets:
Introduction - Sample data sets:

Statistics is just the collection and analysis of data on special aspects of the life of people, helpful to the situation. Fundamental Statistics compacts with collection, organization, analysis and understanding of data. The word statistics has held special meaning in different contexts, hence that the computation process is based on the meaning and datas. In this article we will discuss about sample data sets with some example problems.

Example Problems - Sample Data Sets:

Sample data sets problem 1:

Find out the mean, standard deviation, and variance: 8, 9, 10, 11, 12, 13, 14, 15 and 16

Solution:

(i) Mean: barx = '(sum(x)) / n'

= '(8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16) / 9'

=' 108 / 9 '

' barx = 12'

Variance: S2 = '(sum(x-barx)^2)/(n-1)'

(ii) Then we have to find out the sum of '(X - barx) 2'

'X'

'X - barx'

'(X-barx)^2 '

8

8 12 = -4

16

9

9 12 = -3

9

10

10 12 = -2

4

11

11 12 = -1

1

12

12 12 = 0

0

13

13 12 = 1

1

14

14 12 = 2

4

15

15 12 = 3

9

16

16 12 = 4

16

Total

60

N = 9 is the total number of given values.

Then n-1 = 9 1

= 8

(iii) To place the standard deviation by the method.

S = 'sqrt((X-barx)^2/(n-1))'

= 'sqrt(60)/sqrt(8)'

= '(7.74) / 2.82'

'S = 2.744 '

(iv) Variance = S2

= 2.744 * 2.744

= 7.529536

Sample data sets problem 2:

Find out the mean, standard deviation and variance for the given data: 12, 13, 14, 15 and 16

Solution:

(i) Mean: barx = '(sum(x)) / n'

= '(12 + 13 + 14 + 15 + 16) / 5'

= '70 / 5'

'barx = 14'

Variance: S2 = '(sum(x-barx)^2)/(n-1)'

(ii) Then we have to find out the sum of '(X - barx) 2'

'X'

'X - barx'

'(X-barx)^2 '

12

12 14 = -2

4

13

13 14 = -1

1

14

14 14 = 0

0

15

15 14 = 1

1

16

16 14 = 2

4

Total

10

N = 9 is the total number of given values.

Then n-1 = 5 1

= 4

(iii) To place the standard deviation by the method.

S = 'sqrt((X-barx)^2/(n-1))'

= 'sqrt(10)/sqrt(4)'

= '(3.162) / 2'

'S = 1.581 '

(iv) Variance = S2

= 1.581 * 1.581

= 2.499561

Practice Problems Sample Data Sets:

Sample data sets practice problem 1:

Find out the mean, standard deviation and variance for the given data: 22, 23, 24, 25.

Answer:

S = 1.29

V = 1.66

APA style reporting of statistics for "Results" section:

Sample data sets practice problem 2:

Find out the mean, standard deviation and variance for the given data: 10, 20, 30, 40, and 50.

Answer:

S = 15.81

V = 250

by: jeri

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