State the name given to the smooth, long-term direction shown by a moving average once the seasonal ups and downs have been removed.
(Total for Question 1 is 1 mark)
2
State the name given to a pattern that rises and falls in the same way at the same point in every year, such as ice lolly sales rising every summer.
(Total for Question 2 is 1 mark)
3
Write down whether this statement is True or False. A 4-point moving average is found by adding 4 consecutive data values and dividing the total by 4.
(Total for Question 3 is 1 mark)
4
Write down whether this statement is True or False. A 4-point moving average value is plotted at the same time point as the last of the 4 values used to calculate it.
(Total for Question 4 is 1 mark)
5
Write down whether this statement is True or False. Seasonal variation repeats in exactly the same way, with no exceptions, in every single year.
(Total for Question 5 is 1 mark)
6
The quarterly sales figures for a market stall are 18, 42, 66, 24. Work out the total of these four values.
(Total for Question 6 is 1 mark)
7
The total of four consecutive quarterly sales figures is 150. Work out the 4-point moving average for this data.
(Total for Question 7 is 1 mark)
8
The first three 4-point moving averages for a cafe's quarterly sales are 40, 42, 44. State whether the trend is increasing, decreasing, or roughly constant.
(Total for Question 8 is 1 mark)
9
A shop's quarterly sales are 34, 58, 82, 38. Work out the first 4-point moving average for this data.
(Total for Question 9 is 2 marks)
10
A pharmacy's quarterly sales of sun cream are 12, 46, 78, 24, 18. Work out the second 4-point moving average for this data (using the last four of these five values).
(Total for Question 10 is 2 marks)
11
A garden centre's first two 4-point moving averages for compost sales are 60 and 63. State whether the trend is increasing or decreasing, and give a reason.
(Total for Question 11 is 2 marks)
12
A shop records sales over 2 complete years, giving 8 quarters of data. Work out how many 4-point moving averages can be calculated from this data.
(Total for Question 12 is 2 marks)
13
A bakery has 10 quarters of sales data. Work out how many 4-point moving averages can be calculated from this data.
(Total for Question 13 is 2 marks)
14
The trend line for a cafe's sales has a value of 48 in one quarter, and increases by 3 each quarter after that. Work out the trend value two quarters later.
(Total for Question 14 is 2 marks)
15
A toy shop's quarterly sales of umbrellas are 15, 45, 20, 10, 18, 50. Calculate the first three 4-point moving averages for this data.
(Total for Question 15 is 3 marks)
16
A shop's five successive 4-point moving averages are, in order: 80, 78, 82, 85, 90. State whether the trend is increasing, decreasing or roughly constant, giving a reason using values from the list. A student then claims that these moving averages prove every individual quarter sold more than the quarter before it. Explain why this claim is not necessarily correct.
(Total for Question 16 is 3 marks)
17
A cafe's trend value is 65 in one quarter, and is expected to increase by 4 each quarter. The seasonal variation for the following quarter is known to be -6. Predict the trend value for the following quarter, then use it to forecast the actual sales for that quarter.
(Total for Question 17 is 3 marks)
18
Four successive seasonal variations for a shop's quarterly sales are +12, +28, -15, and an unknown value for the fourth quarter. Seasonal variations for a full year should sum to (approximately) zero. Work out the missing seasonal variation, and state which of the four quarters has the largest positive seasonal variation.
(Total for Question 18 is 3 marks)
19
A garden centre's quarterly bedding-plant sales are 22, 58, 90, 34, 26, 62. Calculate the first three 4-point moving averages for this data, then state whether the trend is increasing, decreasing or roughly constant.
(Total for Question 19 is 4 marks)
20
A shop's trend value is 120 in Quarter 1 of Year 3, and increases by 5 each quarter. The seasonal variations for Quarters 1 to 4 are +10, +30, -15, -25 respectively. Forecast the shop's actual sales for Quarter 3 of Year 3, and comment on one reason this forecast might not be accurate.
(Total for Question 20 is 4 marks)
Mark scheme · S15D Time Series and Moving Averages: Fluency and Exam Drill
B1 valid reason comparing the first (80) and last (90) values, or noting the general rise, oe
B1 explains that moving averages smooth out/remove seasonal variation, so they cannot show whether every individual quarter's raw sales rose, oe
Answer: Increasing (90 is greater than 80, and the values generally rise); the claim is not necessarily correct because a moving average removes seasonal variation and cannot show whether every individual quarter's raw sales rose.
Question 17
M1 65 + 4, oe
A1 69 cao
A1 63 cao ft (69 + (-6))
Answer: Trend = 69; forecast sales = 63
Question 18
M1 12 + 28 - 15, oe (=25)
A1 -25 cao
A1 the quarter with +28 identified as the largest positive seasonal variation, ft
Answer: Missing seasonal variation = -25; the quarter with +28 has the largest positive seasonal variation.
B1 Increasing, ft (since 51, 52, 53 rise steadily)
Answer: 51, 52, 53; the trend is increasing
Question 20
M1 120 + 5 + 5, oe (=130)
A1 130 cao
A1 115 cao ft (130 + (-15))
B1 valid limitation, e.g. unusual weather or a new competitor could make the forecast inaccurate, oe
Answer: Trend for Quarter 3 = 130; forecast sales = 115; for example, unusual weather or a competitor opening nearby could make the forecast inaccurate.