Maths – Statistics

I have been asked to construct an assignment regarding statistics. The statistics of which I will be using will be ‘football attendances’. The football teams I have chosen to use are ‘Birmingham City FC’ and ‘Chelsea FC’. The attendances will be based around the Home league games of the 2010/11 season. I have collected my data from the official websites of both of these teams, which are www.bcfc.com and www.chelseafc.com. I have also used the data-handling cycle to help.The question, which is something which I stated, will be:Do Chelsea FC have more consistent fans than Birmingham City FC?From the chart, table, diagram and graph below we may be able to see variations between the two groups of attendances.Table of AttendancesBirmingham CityChelsea FC21,39441,58927,33340,93122,18641,76123,13841,82826,85041,75226,47441,59324,35741,07225,77041,64228,24240,98224,34141,22222,28740,84624,37941,82923,66041,82528,27041,74127,01340,73426,14240,84828,10841,65626,07241,68127,75941,739As you can see above, there is a variation between the two groups of attendances, although it is too early to tell I feel Chelsea appear to have a higher consistency of attendances.Attendance Bar ChartThis bar chart appears to show Chelsea FC being slightly more consistent, but is still difficult to know. These are also just a few of randomly picked attendances from the groups, so there is no way of knowing who is more consistent as of yet.Line GraphThe above results appear to show Chelsea with the straighter line, meaning they could possibly have the most consistency in attendance. This is still too early to tell without significant proof.This Pie shows the difference between the highest and lowest attendance. The results show the highest attendance with 57% of the pie with 43% for the lowest.This pie also shows the difference between the highest and lowest attendance. These set of results show the highest attendance as 51% and 49% for the lowest attendance. This shows a higher level of consistency for Chelsea, because the gap between the highest and lowest attendance is less.Attendance Frequency Table:Attendance (thousands)20-2525-3030-3535-4040-45Birmingham City FC811000Chelsea FC000019The frequency table shows that Birmingham City attendance goes into 2 groups, whereas Chelsea FC shows their data into just 1 group.So it appears from all of the diagrams, table etc. above, Chelsea FC have more consistent fans, judging by Birmingham City variation, which would therefore mean they are less consistent to reach the same number of attendance each week.Finding the Mean, Median and ModeIn order to find the Mean, I will add all of the attendance numbers together, and divide the number of sets of data I recorded;Birmingham CityMean: 21,394 + 27,333 + 22,186 + 23,138 + 26,850 + 26,474 + 24,357 + 25,770 + 28,242 + 24,341 + 22,287 + 24,379 + 23,660 + 28,270 + 27,013 + 26,142 + 28,108 + 26,072 + 27,759 = 483,775 � 19 = 25,461 is the meanChelseaMean: 41,589 + 40,931 + 41,761 + 41,828 + 41,752 + 41,593 + 41,072 + 41,642 + 40,982 + 41,222 + 40,846 + 41,829 + 41,825 + 41,741 + 40,734 + 40,848 + 41,656 + 41,681 + 41,739 = 787,271 � 19 = 41,435 is the mean.Birmingham’s mean appears as though it is neither near nor far to most of the attendances, for example, it is close to the attendance figure 25,770 but not very close to 21,394. Whereas the Chelsea attendances are very close to the mean, they are never more or less than 1000 of the mean.To obtain the Median, I will gather all the data into numerical order, and find the middle numberBirmingham City21,394/22,186/22,287/23,138/23,660/24,341/24,357/24,379/25,770/26,072/ 26,142/26,474/26,850/27,013/27,333/27,759/28,108/28,242/28,270Median = 26,072Chelsea FC40,734/40,846/40,848/40,931/40,982/41,072/41,222/41,589/41,593/41,642/ 41,656/41,681/41,739/41,741/41,752/41,761/41,825/41,828/41,829Median = 41,642Both Chelsea and Birmingham’s attendance both seem to be closer to the highest attendance than the lowest.The Mode is taken by looking for the most common number, or the number which occurs most often;Birmingham CityMode: 21,394/22,186/22,287/23,138/23,660/24,341/24,357/24,379/25,770/ 26,072/ 26,142/26,474/26,850/27,013/27,333/27,759/28,108/28,242/28,270Mode = No Mode because there is no number that occurs the most.Chelsea FCMode: 40,734/40,846/40,848/40,931/40,982/41,072/41,222/41,589/41,593/ 41,642/ 41,656/41,681/41,739/41,741/41,752/41,761/41,825/41,828/41,829Mode = No Mode because there is no number that occurs the most. Although 41 thousand occurs the most, I feel this cannot be the mode because the ‘hundreds’ after the 41, are not the same. For example; 41,752 and 41,752 would be the mode if this occurred twice, but 41,752 and 41,761 for example are not the same number, although a close match, there is not mode.Both Birmingham and Chelsea have no mode.The differences between the two means are as shown;Football ClubMeanDifferenceBirmingham City25,46115,974Chelsea FC41,435RangeThe range of the two groups of data will be the highest attendance, minus the lowest attendance, when placed in ascending order.Birmingham City28,270 – 21,394 = 6,876 is the Range.Chelsea41,829 – 40,734 = 1,095 is the Range.The range for Birmingham’s attendance is considerably more than that of Chelsea, so you could still say that Chelsea’s attendance is more consistent, because the attendance is always within 1,000 of the highest to lowest attendance compared to Birmingham’s attendance being within 5,939.Cumulative FrequencyBirmingham City;AttendanceFrequencyCumulative Frequency;20,00000;22,00011;24,00045;26,00049;28,000716;30,000319The cumulative frequency diagram shows the Median to be 1/2 of the cumulative frequency maximum, which is 19. So 1/2 � 19 = 9.5th Value. The Median is 26,100. The lower quartile would be 1/4 � 19 = 4.75th value. Lower quartile is 23,900. The upper quartile would be 3/4 � 19 = 14.25th value. Upper quartile is 27,500. So the interquartile range would be 27,500 – 23,900 = 3,600.The interquartile range shows the lower and higher quartiles are within 3,600 of each other.This spread shows a greater spread of data, meaning the data is more varied and less consistent, it is also a shows the attendance to be in a negative skew, which would mean there are more higher values than lower values.Chelsea;AttendanceFrequencyCumulative Frequency;40,00000;41,00055;42,0001419The Median is 1/2 � 19 = 9.5th value. Median = 41,375. The lower quartile is 1/4 � 19 = 4.75th value. Lower quartile = 40,975. The upper quartile is 3/4 � 19 = 14.25th value. Upper quartile = 41,675. So the interquartile range is 41,675 – 40,975 = 700.Both gradients are positive and steep rising. So from the results above this would mean that there is less of a difference between the Chelsea attendances that the Birmingham attendances. Birmingham’s interquartile range is far higher than that of Chelsea, meaning Chelsea’s attendance is more consistent.This spread shows a lower spread of data, meaning the data is less varied and more consistent. This box plot shows that it is a Negative skew, meaning there are more higher values than lower values.ConclusionFrom all of the research and in depth analysis of both Birmingham City and Chelsea attendances, it has been proven that Chelsea have the more consistent attendance in the home league matches of the 2010/2011 season, this does not mean they were more consistent throughout any other seasons, just the season that was examined. I feel I have effectively gathered relevant data and concluded it with relevant proof regarding the consistency of the attendances.

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