Data Analysis Project Descriptive Statistics

Question: Describe about the current era, data analysis is the key element for analysis of any statistical problem? Answer: Introduction: In current era, data analysis is the key element for analysis of any statistical problem. Thus the analysis has to do on the data regarding the time taken to travel to school by Australian students. According to given data it will be look out what average time will required to student to reach the school. Along with that some descriptive statistic for this time variable will be look out. Time to travel to reach the school is given in minutes. Under this study of data for the given variable, we have to see the histogram for this variable. We have to use excel or SPSS for analysis of given data for the variable time required to reach the school for Australian students. Let us see this statistical analysis in detail given below: Data Analysis: In the data analysis part, we have to see some descriptive statistics and histogram for the variable time required for Australian students to reach the school. Descriptive statistics is nothing but the study of mean, mode, median, maximum, minimum, skewness, kurtosis etc. We know that the histogram represents the frequency distribution. In this part, we have to see the histogram for the variable time required for Australian students to reach the school. Let us see the descriptive statistics for the variable time required for Australian students to reach the school. The descriptive statistics for this variable is given below: Descriptive Statistics N Minimum Sum Mean Std. Deviation Variance Time_to_school 125 1.00 2470.00 19.7600 22.97629 527.910 Valid N (listwise) 125 Here, we get the minimum time in minutes for Australian student to reach his school is given as 1 minute. The average time required for reaching to school is given as 19.76 minutes for Australian students. The standard deviation is given as 22.98 minutes. We have to see some other descriptive statistics for the variable time required for Australian students to reach the school which is given in the following table: Descriptive Statistics N Range Maximum Mean Skewness Kurtosis Statistic Statistic Statistic Std. Error Statistic Std. Error Statistic Std. Error Time_to_school 125 149.00 150.00 2.05506 3.148 .217 12.618 .430 Valid N (listwise) 125 There are total 125 students are participated in this survey. Data is collected for the time required to reach the school. The range for time required to reach the school is given as 149 minutes. The maximum time required for reaching to school is given as 150 minutes. Coefficient of skewness describes the skew of the distribution for the variable under study. Here, we get coefficient of skewness as 3.148; this means, coefficient of skewness is greater than zero and it is a positive coefficient. So, we interpret that the given variable time required to reach the school have asymmetrical distribution with a long tail to the right. Here, we get the coefficient of Kurtosis as 12.618, this means, the study variable have a distribution more peaked than a Gaussian or normal distribution. Histogram shows the exact nature of the frequency distribution of the study variable. The histogram for the variable time to reach the school for Australian students is given below: From above histogram we conclude that the variable time taken by Australian student to reach the school have an asymmetrical distribution with a long tail to the right. Interpretations: 1) Average time for Australian students to reach the school is found as 19.76 minutes. 2) Minimum time required for Australian student to reach the school is 1 minutes.3) Maximum time required to reach the school is 150 minutes.4) We conclude that the variable time taken by Australian student to reach the school have asymmetrical distribution with a long tail to the right.5) We interpret that the variable time required to reach the school have distribution more peaked than a normal distribution. References: 1) Robert V. Hogg, Allen T. Craig, Joseph W. McKean, An Introduction to Mathematical Statistics, 6th ed., Prentice Hall, 2004.2) George Casella, Roger L. Berger, Statistical Inference, 2nd ed., Duxbury Press, 2001.3) David R. Cox, D. V. Hinkley, Theoretical Statistics, Chapman Hall/CRC, 1979.4) Peter J. Bickel, Kjell A. Doksum, Mathematical Statistics, Volume 1, Basic Ideas and Selected Topics, 2rd ed. Prentice Hall, 2001.5) T. S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach, Academic Press, Inc., New York, 19676) Harald Cramr, Mathematical Methods of Statistics, Princeton, 1946