Using the above data, calculate the mean, median and mode. Discuss what these statistics measure and why they have different values.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Case Studies

Case Study 1

Every year the population of Edinburgh doubles during the month of August when the famous Edinburgh Festival is held in venues throughout the city. It is the biggest arts festival in the world and contributes significantly to the city’s economy and cultural heritage. You have been hired as an analyst by the festival director to look at a number of different issues from last year’s festival.

Each individual show at the festival makes money through ticket sales and through the sales of paper event programmes to guests once they are in the venue. You have been asked to look at programme sales at one particular show in the Usher Hall in the city centre, which ran for 50 nights. The number of programmes sold each night was as follows:

Number of programmes sold each night

130 171 164 162 145 140 154 166 171 174

140 165 165 151 141 137 138 140 163 158

136 159 165 167 146 149 165 148 155 150

150 160 161 135 157 172 156 134 140 152

132 130 144 173 143 133 130 147 153 139

n = 50

Σx = 7,556

Σx2 = 1,150,276

(i) Using the above data, calculate the mean, median and mode. Discuss what these statistics measure and why they have different values.

(4 marks)

(ii) Find the range, the standard deviation and the quartile deviation. Describe what each of these statistics measures.

(6 marks)

(iii) Construct a grouped frequency table using intervals of five units, i.e. 130–134, 135–139, 140–144, etc.

(4 marks)

 (iv) Use the grouped frequency table to calculate the mean. Compare this value with the one obtained in (i) above and describe why they differ.

(5 marks)

(v) Write a short report on programme sales, highlighting the features of the data. Indicate any further information that should be collected.

(6 marks)

(Total 25 marks)

Attachments:

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