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Question:

Describe about basic statistics?

 

Answer:

Introduction:

We have to check the hypothesis whether there is a relationship between the height and weight of students. We have to also check whether there is any significant relationship exists between GPA and number of hours TV seen by students. We have to see some descriptive statistics for the variables under this study. The list of variables is given below:

Variable number 1: Gender

Variable number 2: Height

Variable number 3: Weight

Variable number 4: GPA

Variable number 5: TV hours

Data is given in the appendix.

Data Analysis:

We have to see some measures of center and measures of variance for the above variables under study. The measures of center and variance for the variable height are given below:

Height

 

 

 

Mean

67.5

Standard Error

0.783044

Median

67

Mode

64

Standard Deviation

3.501879

Sample Variance

12.26316

Kurtosis

-0.79766

Skewness

0.196093

Range

12

Minimum

61

Maximum

73

Sum

1350

Count

20

Largest(1)

73

Smallest(1)

61

Confidence Level(95.0%)

1.63893


Height has a distribution skewed at positive side.

The measures of center and variance for the variable weight are given below:

Weight

 

 

 

Mean

145.35

Standard Error

6.880665

Median

135

Mode

130

Standard Deviation

30.77127

Sample Variance

946.8711

Kurtosis

6.571934

Skewness

2.152676

Range

145

Minimum

105

Maximum

250

Sum

2907

Count

20

Largest(1)

250

Smallest(1)

105

Confidence Level(95.0%)

14.4014


Weight has a distribution skewed at positive or right side.

The measures of center and variance for the variable GPA are given below

GPA

 

 

 

Mean

3.5955

Standard Error

0.072197

Median

3.755

Mode

3.8

Standard Deviation

0.322873

Sample Variance

0.104247

Kurtosis

-0.8908

Skewness

-0.78316

Range

1

Minimum

3

Maximum

4

Sum

71.91

Count

20

Largest(1)

4

Smallest(1)

3

Confidence Level (95.0%)

0.151109


GPA has a distribution skewed at negative or left side.

The measures of center and variance for the variable number of TV hours are given below:

TV Hours

 

 

 

Mean

2.075

Standard Error

0.480234

Median

2

Mode

2

Standard Deviation

2.147673

Sample Variance

4.6125

Kurtosis

1.802421

Skewness

1.457529

Range

7.5

Minimum

0

Maximum

7.5

Sum

41.5

Count

20

Largest(1)

7.5

Smallest(1)

0

Confidence Level(95.0%)

1.005142


The variable TV hours has a distribution skewed at positive or right side.

The correlation coefficient between height and weight is given below:

 

Height

Weight

Height

1

 

Weight

0.737281

1


There is strong association exists between height and weight of a students.

The correlation coefficient between GPA and TV hours is given below:

 

GPA

TV Hours

GPA

1

 

TV Hours

0.1785

1


There is weak association exists between GPA and number TV hours.

Real life applications:

Mean: Most of the time we use the word average percentage of a students in a particular school is high. We sometime say’s the average time for cooking a particular food is 15 minutes.

Mode: A bakery that sells twice as many red velvet cupcakes as chocolate brownies will need to produce more cupcakes to satisfy their customers. In this bakery, the number of red velvet cupcakes sold is the mode.

Median: When we have information about the group of people with some age group, then we consider the middle value or median as a representative age of this group.

 

References:

  • David Freedman, Robert Pisani, Roger Purves, Statistics, 3rd ed., W. W. Norton & Company, 1997.

  • Morris H. DeGroot, Mark J. Schervish Probability and Statistics, 3rd ed., Addison Wesley, 2001.

  • Leonard J. Savage, The Foundations of Statistics, 2nd ed., Dover Publications, Inc. New York, 1972.

  • Robert V. Hogg, Allen T. Craig, Joseph W. McKean, An Introduction to Mathematical Statistics, 6th ed., Prentice Hall, 2004.

  • George Casella, Roger L. Berger, Statistical Inference, 2nd ed., Duxbury Press, 2001.

  • David R. Cox, D. V. Hinkley, Theoretical Statistics, Chapman & Hall/CRC, 1979.

  • Peter J. Bickel, Kjell A. Doksum, Mathematical Statistics, Volume 1, Basic Ideas and Selected Topics, 2rd ed. Prentice Hall, 2001.

  • S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach, Academic Press, Inc., New York, 1967

  • Harald Cramér, Mathematical Methods of Statistics, Princeton, 1946
OR

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