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# Basic Statistics Assignment

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## Question:

### 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

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