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:
The 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 Mode
In 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 City
Mean: 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 mean
Chelsea
Mean: 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 number
Birmingham City
21,394/22,186/22,287/23,138/23,660/24,341/24,357/24,379/25,770/26,072/ 26,142/26,474/26,850/27,013/27,333/27,759/28,108/28,242/28,270
Median = 26,072
Chelsea FC
40,734/40,846/40,848/40,931/40,982/41,072/41,222/41,589/41,593/41,642/ 41,656/41,681/41,739/41,741/41,752/41,761/41,825/41,828/41,829
Median = 41,642
Both 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 City
Mode: 21,394/22,186/22,287/23,138/23,660/24,341/24,357/24,379/25,770/ 26,072/ 26,142/26,474/26,850/27,013/27,333/27,759/28,108/28,242/28,270
Mode = No Mode because there is no number that occurs the most.
Chelsea FC
Mode: 40,734/40,846/40,848/40,931/40,982/41,072/41,222/41,589/41,593/ 41,642/ 41,656/41,681/41,739/41,741/41,752/41,761/41,825/41,828/41,829
Mode = 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;
Range
The range of the two groups of data will be the highest attendance, minus the lowest attendance, when placed in ascending order.
Birmingham City
28,270 - 21,394 = 6,876 is the Range.
Chelsea
41,829 - 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 Frequency
Birmingham City;
The cumulative frequency diagram shows the Median to be ½ of the cumulative frequency maximum, which is 19. So ½ × 19 = 9.5th Value. The Median is 26,100. The lower quartile would be ¼ × 19 = 4.75th value. Lower quartile is 23,900. The upper quartile would be ¾ × 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;
The Median is ½ × 19 = 9.5th value. Median = 41,375. The lower quartile is ¼ × 19 = 4.75th value. Lower quartile = 40,975. The upper quartile is ¾ × 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.
Conclusion
From 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.
References:
www.bcfc.com
www.chelseafc.com