Download Analysis of Hotel Stays, Shoe, Console, Laptop, Chocolate Egg Sales, and Course Enrollment and more Exams Fourier Transform and Series in PDF only on Docsity!
1. The table gives information about the number of people staying in a hotel each quarter in 2011 and in 2012. Year 2011 2012 Quarter 1 2 3 4 1 2 3 4 Number of people 261 353 372 290 193 309 292 202 ( a ) Calculate the 4-point moving averages for this information. The first three have been done for you. 319, 302, 291, .......................... , .......................... (2) The information in the table is shown on the grid. ( b ) On the grid, plot the 4-point moving averages. (2) ( c ) Describe what the moving averages show about the trend in the number of people staying at the hotel over this period. ...................................................................................................................................................... (1) (Total for Question 1 is 5 marks) 2. The table shows information about the numbers of shoes sold in a shop.
Year Quarter Number of Shoes 2010 1 255 2 309 3 285 4 243 2011 1 294 2 330 ( a ) Calculate the 4-point moving averages for this information. ........................... ........................... ........................... (2) ( b ) Describe what the moving averages show about the trend in the numbers of shoes sold in the shop over this period of time. ...................................................................................................................................................... (1) (Total for Question 2 is 3 marks)
3. The table shows information about the number of games consoles sold each month by a shop.
Month January February March April May Number of laptops
( a ) Work out the 3-point moving averages for the first five months of 2012. .................... .................... .................... (2) The 3-point moving average of the number of laptops sold in April, May and June of 2012 was 2300. ( b ) Work out the number of laptops sold in June 2012. .......................................... (2) ( c ) Describe what the moving averages show about the trend in the number of laptops sold in the shop in the first six months of 2012. ................................................................................... (1) (Total for Question 4 is 5 marks) 5 The time-series graph gives information about the number of chocolate eggs sold in a shop each quarter in 2013 and in 2014.
( a ) Calculate the 4-point moving averages for the information in the graph. You must show your working. The first three have been done for you. 240, 257.5, 277.5, ......................................... , ......................................... (3) ( b ) Describe what the moving averages show about the trend in the number of chocolate eggs sold in the shop during this period. .................................................................................. (1) (Total for Question 5 is 4 marks)
6. The table gives information about the number of students who enrol for a course in each term in 2011, in 2012 and in 2013. The 3-point moving averages are given correct to 3 significant figures.
( c ) On the time-series graph, draw a trend line for the 3-point moving averages. (1) ( d ) (i) Use your trend line to find an estimate for the mean seasonal variation in numbers enrolling for the Autumn Term. .......................................... (2) (ii) Predict the number of students who will enrol in the Autumn Term of 2014. .......................................... (2) (Total for Question 6 is 9 marks)
7. This time-series graph gives information about the quarterly electricity bills paid by a household from 2010 to 2012. A trend line has been drawn on the graph. ( a ) Describe the trend. ...................................................................................................................................................... (1) ( b ) Work out the seasonal variation for quarter 2 of 2012. .......................................... (2) (Total for Question 7 is 3 marks)
( b ) Describe the trend shown by the moving averages. ....................................................................... (1) ( c ) (i) Find an estimate for the mean seasonal variation for quarter 1. .......................................... (ii) Work out an estimate for the number of cameras sold in quarter 1 of 2015. .......................................... (4) (Total for Question 8 is 8 marks)
9. The time–series graph shows information about the number of tourists who visited a museum each quarter for the years 2012, 2013 and 2014. The graph also shows the 4-point moving averages for this information. A trend line for the moving averages has been drawn. ( a ) Describe the trend. .................................................................................... (1) ( b ) Calculate the mean seasonal variation for quarter 1. .......................................... (2) (Total for Question 9 is 3 marks)
