Understanding Statistics: Concepts and Methods - Assignment Example

Statistical Report Name: Course: Tutor: Date: Table of Contents Table of Contents 1 Introduction 2 Accumulative Analysis table 4 Pareto Chart 5 Data collection 7 Percentage rations 8 The control chart 11 Root Cause Analysis 14 Conclusion 15 Introduction In 2010 a school in named Chemamul Academy was establish with four streams per class. The department in charge of academics is assign with the role of establishment of the department was mainly to screen on numerous academic barriers which harmed the school’s performance. It was a private institution; the public institution is not easily assessed at the school level. Like any other business organization, it was aimed at providing performance services to the pupils who were learning in the institution (Black, 2009). Price was not linked in any way with quality. Since its establishment, the school has been using all their efforts in order to ensure that pupils are attaining high performance. They are also aimed at meeting the requirements of international market so that they can achieve the ISO 9001:2008 and in respect to this, a lot of efforts are required in order to achieve these international standards, the key thing is to improve on the services of the academy. In their efforts, teachers and other non-teaching staff should also put into much concern just as the parents are being satisfied (Brase & Brase, 2011). Managers in charge of academics at Chemamul Academics saw their need to conduct a survey in their four streams which were subdivided for all the pupils to get access to performance education without any disturbance. The results that were collected did not impress the managers as the performance was poor which did not impress the parents and Board of Governors. In order to consider Chemamul Academics as quality, timeliness has been considered a major factor. The duration in which assignment took from the time it was issued to the time when they were assessed was long. In May 2011, the number of assignment that was received at the academic office was 200 and was distributed as follows in the four streams (Dalgaard, 2002). Ratio Pie Chart North- 60 South- 40 East- 70 West -30 Figure (a): pie chart illustrating percentage of assignments for the four streams in may 2011. As indicated in the pie chart, it is an illustration of how the 200 assignments were received in May 2011 was distributed to the four streams of Chemamul academy. It is clear to say that most of the assignments were from the East as it had the highest percent of 35% followed by North with 30%. Out of the survey that was carried out concerning the satisfaction of the pupils which was conducted in May 2011 reveals that out of 200 assignments that were received, there were 30 complaints that represent delaying in time of collection to the academics department as they were not collected at the required time. The table below illustrates the number of complaints and their percent of complaints to each stream; it also gives an illustration of those complaints among various academics fighting streams as presented in the table below. Most of the complaints emanated from NORTH stream and more intervention was required from the performance department. Accumulative Analysis table Academics fighters time of collection complaints (May ) Academics fighting stream No of complaints Percent of complaints Accumulative percent North 12 40% 40% South 9 30% 70% West 6 20% 90% East 3 10% 100 Total 30 100% 100% Figure (b): the table is an initial data for the complaints Pareto Chart Figure (c): Pareto chart for delaying time of collecting assignments As per the Pareto chart, North stream presents a good study so as to come up with causes and factors that were contributed to increase the number of complaints that represent the level of performance and satisfaction of the pupils. In order to improve on performance outcomes through daily practical work with pupil’s it is require of us to first try and reduce the time of submission to any emergency assignments. This could happen by defining the concept of time of submission. In academics fighting, time of assignment submission is basic assignments the time from which assignment is issued by the academic department until arrival to the office. It is measured by the number of minutes from issuing assignment to the time at which the academics department receive the assignment. What is therefore required of us is to understand receiving assignment that clarifies the process from receiving assignment to the time at which the academics is assessed (McClave & Sincich, 2006). Figure (d): Flow chart of assignments process Data collection The performance managers at Chemamul Academy decided that they had to initiate a separate survey about East as one of its streams in order to determine the causes that led to the delay in time of collection to attend to this reasons and causes by proper interventions. In this process, the first move was to collect the required data concerning the stream; the data are then divided into two sections and are identified by letters Q and P. Letter Q represent those regions that are far from the stream; should be as far as 25 kilometers and below. P on the other hand, represents regions that are far fro the stream of up to 50 kilometers. Percentage rations According to the pie chart, NORTH represents 45% of the total assignments which were recorded for the four streams in May 2011 which represents 180 assignments that were directed to this stream as the total assignments were 200. The 180 assignments are then distributed to the two regions. Figure (e): percentage of assignments for region Q and P. Basing on the pie chart above, the two regions have a difference of 20% from one another as per the number of assignments; region Q has 108 while region P has 72 assignments; the difference being 30 assignments (Urdan, 2005). The two tables below will be analyzed in detail with the need to give a better understanding. The tables illustrate a sample of 30 assignments and the time that will be required in order to reach each of the selected samples. The tables below are the key data in order to establish further diagrams to assess the performance and to determine key processes which need more attention. Region Q assignments May 2011 Assignment Time needed in minutes Assignment Time needed in minutes 1 10 16 12 2 13 17 8 3 8 18 12 4 14 19 11 5 12 20 15 6 15 21 12 7 17 22 16 8 14 23 14 9 15 24 9 10 11 25 10 11 16 26 13 12 15 27 9 13 8 28 13 14 14 29 10 15 14 30 13 Table (a): data for assignments and time required for region Q. Region P assignments May 2011 Assignments Time needed in minutes Assignments Time needed in minutes 1 12 16 10 2 8 17 13 3 12 18 8 4 11 19 14 5 15 20 12 6 14 21 15 7 16 22 17 8 11 23 9 9 8 24 14 10 17 25 10 11 13 26 16 12 9 27 15 13 13 28 8 14 10 29 14 15 16 30 12 Table (b): data for assignment and time required for region P. The control chart The control chart that was used was the X-bar chart, the reason was that the data which were used were variables and not attributes. In addition, the chart is a tool that is used to monitor the condition of continuous variable process (Shao, 2005). In order to come up with a good control chart, calculation of values of sample mean, standard deviation and upper control limits are to be done after which a lower control limit ca not be determined since it does not apply to this type of data mainly because the lower time is preferred to be good as time of collection . A zero value will therefore be determined to act as a bottom line. Warning lines can also be calculated so as to give us the areas of defects. The data is the two tables will be referred to though separately. A sample mean, standard deviation, UCL and UWL are calculated and plotted at the control chart as illustrated below. Starting with region Q, mean was 12.4 minutes, standard deviation 2.57. UCL was calculated by referring to the 3 sigma rule, value of it equals to 14 minutes. UWL was calculating by assuming 2 sigma and equals to 14.1. Figure (f): control chart for region Q The values plotted at the control chart above are a clear indication that there were 7 values which are out of control, assignments number 17, 17, 15, 16, 15, 16 and 15. Apart from these there are other assignments that exceeded the warning limit. Moving to region P, another 30 sample have been chosen as illustrated in table (b) above from a total of 72 populations, other measures were calculated and they were shown as follows: As for the mean it was 13.4 minutes, standard deviation 2.8, and the UCL which is 11.2 and the UWL which equals to 12.7. Figure (g): Control chart for region P According to the illustration above, the number of values that exceeded control is 8 assignments; they are samples; 15, 16, 1715, 16, 17, 16 and 16. There are other five points that exceeded control limits but below the warning limit are 13 and 13. An X-bar chart had been established earlier which was plotted as a control chart. The reason for the chart to be established was to monitor the points that are out of control with much ease. Others that were to be included in the control chart were behavior and values. The total percentage of the points that exceeded control of the two control charts were 25% meaning that ¼ for each of the regions can not accept anywhere, which need that a further investigations to the problem be analyzed in order to adjust to the problem. In relation to that therefore, a fishbone diagram was considered for further examination to the issue. Root Cause Analysis The analysis of control chart brought a bout a backup on how the problem could actually be solved as a meting was assignments after the key elements were identified through the control chart. The aim of the meeting was to come up with solutions to the remaining quarter of the problems. Traffic jams Lack of proper training Covering long distance Poor attitude Stuck in mad and snow Failing to report to work Misunderstanding mechanical failure Poor networks vehicle accident New places and new address insufficient fuel Conclusion The lateness was later realized to be caused by number of reasons; poor weather conditions that caused, traffic overloads, sticking, in mud and also covering long distances. It was also clear according o the findings that there existed a misunderstanding between the staff due to poor communication. Moreover, in order to avoid lateness, staff should undergo a proper training, in training them; they will have a positive attitude to their duties. Absenteeism is as a result of negative attitude towards work, if they are well trained and well rewarded, they will never fail to report work. Sometimes, there vehicles are prone to accidents due to mechanical problems. Proper servicing has to be dome before they go to work to avoid lateness at the time of emergency. Fuel being another cause is all about finances, vehicles should be daily checked if their fuels tanks are full, and also extra fuel should be stored to avoid rushing at the time of emergency. Bibliography Black, K 2009, Business Statistics: Contemporary Decision Making, 6th edn, JohnWiley & Sons. Brase, CH & Brase, CP 2011, Understanding Statistics: Concepts and Methods, 10th edn, Cengage Learning. Dalgaard, P 2002, Introductory statistics with R, Illustrated edn, Birkhauser. McClave, JT & Sincich, T 2006, Statistics, 10th edn, Pearson, Prentice Hall. Shao, J 2005, Mathematical statistics: exercises and solutions, illustrated edn, Birkhauser. Urdan, TC 2005, Statistics in Plain English, 2nd edn, Routledge. Read More