Business Statistics Questions - Assignment Example

Question A is considering introducing a third semester so that can complete their degrees in 2 years, by remaining at the university over the summer vacation. To help the university decide whether this would be acceptable to staff and students, it wants to conduct a survey to establish the views of a cross-section of the university community. (a) In the context of this problem, describe the terms: Target population is the entire group where we would like to draw our conclusions from, in this case the university staff and students. Sampling frame is the actual set of components from which a sample is drawn. Ideally this should match with the population of interest e.g. for a simple random sample all individuals from the sampling frame must have an equal chance of being drawn into the sample. Stratified sampling is the process of separating a heterogeneous population into homogeneous sub-groups (strata) from which we expect to find measurements of interest. The assumption here is that the proportion of each sub-group in the sample is the same for the population. Cluster sampling is the technique when a random sample would produce a very wide and scattered list of subjects such that instead the population is divided into clusters then a random sample of the clusters is selected for observation. Random Sampling is the technique of selecting a group of subjects from a population purely by chance regardless of whether the likelihood to be selected is equal or non-equal (McClave & Benson, 1995). This technique eliminates bias. (b) Design 5 questions that you might ask the respondents to the survey. Explain how these questions would help you satisfy the aims of the survey. Question one: In your opinion, how long should it take for you to obtain a degree with us? This is a very open ended question that would target the student population and would preferably be accompanied by options such as 3years, 2years+summer classes, 4 years with an internship year in between etc. From such options the students would choose from a choice board provided by the university. They will choose something that the university is ready and willing to do. Question two: Do you think shortening our degree courses will make the university more or less competitive? This question would target the university staff because the competitiveness of a university motivates them to stay or move on to other universities. From the staff opinion it would be easier to gauge whether they would buy in to the 2 year degree programme or not. Question three: Are you willing to take a summer course? This question would target the student population and would elicit Yes/No answers that would gauge the general attitude of the student population. Question four: Are you willing to lecture in summer? The university lecturers cooperation is essential for the project to take off therefore the university would need to see how many of its lecturers are up to the task. From this reply the university would know if it needs to entice lecturers to buy-in or not. Question five: Can you afford schooling during summer? Many students take on summer jobs to assist them meet the financial obligations that come about from joining a university or to help them reduce their student loans. Thus the question of affordability would be critical for the university. The university would not want to start a program that its students cannot afford to join. (c) What type of data collection method would you use (postal, telephone or face to face)? I would use a face to face data collection method because firstly of the setting. University students would be very unwilling to fill questionnaires and post them back and also they would not be so cooperative over the telephone. It is also easier to assess their attitude and ensure their concentration in a face to face interview. Question 2 Table below shows how the sales of Marla plc were broken down between the company’s four sales regions during the years 2004 to 2008. Marla Sales Information Sales Region Year ( Sales £m) 2004 2005 2006 2007 2008 S. West 4.0 2.0 2.2 3.6 3.7 South 6.0 4.9 2.5 3.2 3.7 S. East 7.6 9.1 5.2 4.3 4.2 Wales 1.5 1.4 1.4 1.5 1.6 Totals 19.1 17.4 11.3 12.6 13.2 (a) Draw a simple bar chart to show the total sales for the four year period (b) Draw a component bar chart to show the sales for the years and how they were broken down between the four sales regions. (c) Draw a pie chart to show the breakdown of total sales in 2008. (d) What can you conclude about the sales of Marla plc? From the charts above we can conclude that: Total sales per year have declined (see chart: Total sales by year) from £19.1M in 2004 to £13.2M in 2008. In spite of the overall decline in sales S. East region continues to dominate in sales totals, 32% in 2008 (see sales per region for 2008 pie chart). The S. East region may be dominant but it has also had the highest decline in sales from £9.1M in 2005 to £4.2M in 2008. This could be the cause of the overall decline considering that the S. East region has the highest share of sales contribution to the company. Wales has a steady sales total over the five year period. 2006 saw the company’s worst sales performance, £11.3M while its best was in 2004, £19.1M Question 3 A survey of workers in a particular industrial sector produced the following table: _______________________________ Income ( weekly) Number _______________________________ £50 to £100 170 £101 to £150 245 £151 to £200 237 £201 to £250 167 £251 to £300 124 ________________________________ (a) Calculate the mean, median, mode and standard deviation. Income (weekly) Frequency £50 to £100 170 £101 to £150 245 £151 to £200 237 £201 to £250 167 £251 to £300 124 Median 170 Mode 245 Mean 188.6 Standard Deviation 51.25 (b) Explain the advantages and disadvantages of using mean, median and mode to analyse data. Mean is the probably the most commonly used statistic of all time. It is one way to determine where the centre of the data is. Its advantage is that all values in a data set are taken into account (Triola, 2007).However, the disadvantage of using mean is that it is affected by outliers - numbers in the data set that are extremely high or extremely low compared to the rest of the data. The median of a data set is the value that lies exactly in the middle when we order the numbers from smallest to largest (Ramsey, 2003). The advantage of using the median is that it is not affected by outliers. In fact, the most governments often use the median to represent the centre with respect to their data because of the extreme values in various national data. The disadvantage of using median is that for a data set with even number of items one cannot find a middle value therefore a compromise in form of the ‘average of the two middle values’ is used. Mode is the most frequently occurring value in the data set and its advantage is that it is not affected by extreme values. Mode is also useful where a data set has more than one frequently occurring values (Jaisingh, 2000). The disadvantage of mode is that it cannot be used in data sets where values do not occur more than once. References McClave, J. T & Benson, G. (1995). A First Course in Business Statistics (6th ed.). Engelwood Cliffs, NJ: Prentice Hall. Rumsey, D. (2003). Statistics for Dummies. New York: John Wiley & Sons Triola, M. F. (2007). Elementary Statistics (10th ed.). New York: Benjamin-Cummings Publishing Co. Jaisingh, L. (2000). Statistics for the Utterly Confused. New York: McGraw-Hill Read More