Analysis and Forecasting of Food Venue Data and Ticket Sales

Calculating the Mean, Standard Deviation, and Quartiles

Q 1 You have been given the data on how much a selection of adults spent on food at four venues – A, B, C and D.  The data for each venue has been put into groups – see below.

a)Calculate the mean for each of the venues A, B, C & D individually. Enter these values into the on-line test.

b)In your report explain what the mean is, how it was calculated, how it would have been calculated differently if the data had been raw data, and comment on the accuracy of the calculated values.  You need to include an example to help with your explanations.

c)Draw a suitable chart that compares the mean values for all four venues and add this chart to your report.  Fully justify your choice of chart.  Include a second chart showing the same data, but this time choose a less suitable chart, and fully explain why this is the case.

d)Combine all four venues grouped data.  For example, in the group 3 to under 6, A is 7, B is 3, C is 50 and D is 129, so the total will be 189 in this group.  Complete for the remaining groups. Enter these values into the on-line test.

e)For the new combined group calculate the mean and standard deviation.  Enter these values into the on-line test. 

f)Draw a histogram for this combined group, copy this into your report and comment on both the shape of the histogram and what this implies about the calculated mean.     

g)Draw an Ogive and read off the value of the Median, Q1 and Q3.  Calculate the SIR. Enter these values into the on-line test.

h)In your report explain to your manager what the median and quartiles are, and what these combined group values that you have just read from your Ogive actually mean in relation to the scenario.

i)The standard deviation for venue B alone is £3.18.  Compare this value with the one you have calculated from the combined data, and briefly explain why the values are different and what this difference says about the distribution of the data in both venue B and the combined venues.

Q2 (a)You have been asked to forecast the number of adults that will buy tickets in 2020.  With any forecasts there will be concerns for accuracy, and your manager would like you to provide him with an explanation of the four general types of errors that could be in your forecasts.  Also include an assessment of two other (random) factors that may affect the number of tickets sold but have not been included in your forecasts.

Use the headings in your workbook for this answer, but explanations must be in your own words.  Make sure that you relate your answers to the scenario.         

b)You have been provided with the following historical data.

Conduct a time series analysis of the data (using methods as in your statistics notes and a spreadsheet) and determine a range of forecasts of the likely number of adult guests that will attend our venues in 2020.   

i) The trend values for 2016 Q4 and 2018 Q1

ii) The average seasonal variation values for each quarter.

c)In your report clearly state what model choice you have made, and why.  A copy of your graph annotated appropriately is required.

d)Place a copy of your final graph into your report clearly showing your labelled projected trend lines.  Briefly explain the rationale behind the positioning of these lines to your manager.

Present your final forecasts in a suitable table showing ONLY the forecasted values, and have a total for the year.  Take care with presentation of the values!