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QUESTION 10 Which of the following graphs represents a time series plot with a three-point moving average? (A) 20 —e—original data 15 -3 - smoothed data Number 10 5 0 I ] S Q (B) 20 15 —e—original data -3- smoothed data Number 10 ON <t O o0 S o <t \O < > - o — — — — O S S S ) S O S [@\| o o o o o o o Year ©) 20 . ——original data 15 - - smoothed data Number 10 5 0 I (] S [@\| (D) 20 15 —e—original data -3 - smoothed data Number 10
QUESTION 4 (5 marks) The following data shows the profits per quarter for a company for the last two years. Quarter Profit ($°000s) Deseasonalise the data and plot this on the same set of axes as the original data in the graph on the next page. Profit ($°000s) 190 180 170 160 150 140 130 120 110 100 90 80 70 60 > Ql Q2 Q3 Q4 Ql Q2 Q3 Q4 ———-— 2018 ———— e ) =]
QUESTION 1 The second smoothed value for the 3-point moving average is Day | 123|456 awe | 5 [0 w9 0w (A) 32 (B) 25 (C) 20 (D) 18
QUESTION 24 (3 marks) The population of fish in a fish farm pond was recorded every three months. The graph shows the data. 1400 1200 1000 800 600 Population of fish 400 200 0 4 8 12 16 Quarters Describe the time series plot by identifying three key features.
QUESTION 3 The table shows the minimum and maximum temperatures on January 1 each year in Bundaberg. (A) ©) Temperature (°C) Temperature (°C) N N 24 23 22 21 2017 2018 2019 2020 2021 Year 2017 2018 2019 2020 2021 Year (B) (D) Which time series plot best represents the mean temperatures? Temperature (°C) Temperature (°C) 33 U DN 31 30 29 28 2017 2018 2019 2020 2021 Year 2017 2018 2019 2020 2021 Year
QUESTION 19 (4 marks) The graph shows the amount of rainfall (in mm) for each quarter from 2016 to 2021. 250 200 e g = 150 g s (2 o = 100 o £ < 50 O i | | | i ' | i | | | | | i | | | i 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 | | | ] L 1 2016 2017 2018 2019 2020 2021 Quarters (each year) a) Describe the long-term trend and seasonality of the time series data. [2 marks] b) A least-squares line was fitted to the data with y representing the amount of rainfall and x representing the number of quarters since the beginning of 2016 (e.g. x = 5 for the first quarter of 2017). y=1.763x+ 156.5 Interpret the y-intercept and slope of the fitted line. [2 marks]
QUESTION 1 (4 marks) The table shows a swimwear company’s seasonally adjusted swimsuit sales (in thousands). Season e Seasonally adjusted swimsuit sales (in thousands) The long-term seasonal indices for spring summer and winter are 1.11 1.42 and 0.62 respectively. Determine the actual swimsuit sales for autumn.
QUESTION 2 A time series plot is shown. Profit ($’000) oO 0 2 + 6 8 10 12 14 16 Time (years) It could best be described as (A) cyclical. (B) seasonal. (C) irregular. (D) increasing.
QUESTION 10 Annual sales data and related quarterly indices are shown. The quarterly indices were calculated by applying the average percentage method using the mean. 0 Determine the values for x and y.
QUESTION 2 (4 marks) Buffalo fly bites cause skin wounds on cattle. The table shows the average number of skin wounds per animal in a herd for two years. Deseasonalise the data.
QUESTION 12 Quarterly sales figures for a company between 2005 and 2017 were used to determine the following seasonal indices. First quarter Second quarter Third quarter Fourth quarter Swimia | s || o | The table below shows the sales figures for 2018. Season First quarter Second quarter Third quarter Fourth quarter Sales figures ($) 450 075 497 660 480 085 505 025 Determine the seasonally adjusted sales figure for the second quarter of 2018 to the nearest dollar. (A) $428 643 (B) $448 342 (C) $472 579 (D) $552 403
QUESTION 20 Fitting a least-squares line to create a model from a set of time series data ensures that (A) the distances between the data points and the line of best fit are minimised. (B) the same number of data points are above and below the line of best fit. (C) the distances between the data points and the axes are minimised. (D) the least-squares distances of all data points are added together.
QUESTION 9 (4 marks) The table below shows the seasonally adjusted rainfall data (in mm) for a town in Australia. 2015 2016 Summer 96.77 101.61 Winter 100.00 101.39 Spring 100.97 102.91 Autumn 98.04 101.96 The seasonal indices are shown in the table below. Summer 1.24 i Spring 1.03 In 2017 the actual rainfall in summer was 127 mm autumn was 106 mm winter was 75 mm and spring was 107 mm. Analyse the data to predict the total rainfall for each season in 2025.
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