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Statistics Coursework

Extracts from this document...

Introduction

The topic I am investigating for my coursework is about used cars. The data I am using for this investigation is secondary data; this data has been given by the teacher. I took a sample of 40 data out of 204 by using a random number generator on a calculator; this is how I got each number: (SHIFT) Ran# * 204 (Total Population) = Random Number The reason as to why I decided to do random sampling is because it's fair and is not bias; furthermore, every member of the population has an equal chance of being selected. If I got the same number twice, I would do the process again to get a different number. Below is a table of all the numbers I got using a "random number generator" on a calculator: Actual Random Number Nearest to Whole Number Ran# * 204 = 34.254 34 Ran# * 204 = 165.799 166 Ran# * 204 = 64.18 64 Ran# * 204 = 29.360 29 Ran# * 204 = 79.433 79 Ran# * 204 = 138.694 139 Ran# * 204 = 21.855 22 Ran# * 204 = 197.44 197 Ran# * 204 = 56.231 56 Ran# * 204 = 26.074 26 Ran# * 204 = 149.762 150 Ran# * 204 = 138.03 138 Ran# * 204 ...read more.

Middle

Used �665.00 �755.00 �900.00 �1,005.00 �1,155.00 �1,320.00 �1,425.00 �1,620.00 �1,735.00 �2,310.00 �2,665.00 �2,780.00 �3,080.00 �3,335.00 �4,550.00 �4,635.00 �4,915.00 �4,980.00 �5,050.00 �5,645.00 �6,145.00 �6,215.00 �7,100.00 �7,355.00 �7,570.00 �7,675.00 �7,735.00 �7,985.00 �8,230.00 �8,500.00 �8,595.00 �10,075.00 �10,555.00 �11,395.00 �12,150.00 �12,960.00 �13,570.00 �15,755.00 �19,345.00 �25,810.00 LQ: Lower Quartile: (40 / 4) * 1 = 10th number = �2310 UQ: Upper Quartile: (40 / 3) * 3 = 30th number = �8500 IQ: Interquartile Range: UQ - LQ = �8,500 - �2,310 = �6190 IQ * 1.5 = �6190 * 1.5 = �9285 LQ - �9285 = �2310 - �9285 = - �6975 UQ + �9285 = �8500 + �9285 = �17785 Therefore, any value below - �6975 and above �17785 is an outlier. Outliers: �19345 : �25810 The outliers are shown in red in the scatter diagram. Now, I am going to calculate any outliers for the mileage. I am going to do this by completing the same process: LQ: Lower Quartile: (40 / 4) * 1 = 10th number = 12000 UQ: Upper Quartile: (40 / 3) * 3 = 30th number = 49000 IQ: Interquartile Range: UQ - LQ = 49000 - 12000 = 37000 IQ * 1.5 = 37000 * 1.5 = 55500 LQ - 55500 = 12000 - 55500 = - 43500 UQ + 55500 = 49000 + 55500 = 104500 Therefore, any value below - 43500 and above 104500 is an outlier. ...read more.

Conclusion

6 36 �1,320.00 35 10000 28 7 49 �1,155.00 36 10000 28 8 64 �1,005.00 37 10000 28 9 81 �900.00 38 10000 28 10 100 �755.00 39 10000 28 11 121 �665.00 40 3000 30 10 100 Using the data above, I am going to calculate the Spearman's coefficient of rank correlation using this formula: After calculating the Spearman's coefficient of rank correlation, my calculations show a strong positive correlation. My hypothesis is: the car price decreases when the mileage increases. Looking at the scatter diagram without the outliers, it shows a negative correlation, however, when I calculated the Spearman's coefficient of rank correlation, the results I received where contradicting the results from the scatter diagram. Therefore, the results from the scatter diagram, prove my hypothesis. On the other hand, the results from the Spearman's coefficient of rank correlation disprove my hypothesis. Improvements: * Use a cumulative frequency diagram as well as a scatter diagram to find the outliers, Spearman's coefficient of rank correlation etc. * Use a cumulative frequency diagram to accurately find the lower quartile, upper quartile, inter-quartile range. * The data sheet would be more reliable and appropriate if it had no data missing, like in this secondary data provided by the teacher. ?? ?? ?? ?? Statistics Practise Coursework Used Cars Data ...read more.

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