Moving Averages – Page 2

QTB – May 2016 – L1 – SB – Q6b – Operations Research

This question involves calculating seasonal adjustments based on moving average analysis for sales data.

Question

i. The following moving average analysis is obtained for the quarterly sales of a bakery based on the additive model:

Quarter	Trend	Actual Sales in the Quarter	Variation (Actual – Trend)
Year 1: Q3	29.375	29	-0.375
Year 1: Q4	33.125	33	-0.125
Year 2: Q1	37.125	37	-0.125
Year 2: Q2	41.250	41	-0.250
Year 2: Q3	45.000	46	1.000
Year 2: Q4	47.875	48	0.125
Year 3: Q1	53.000	51	-2.000
Year 3: Q2	57.125	58	0.875

Required:
Calculate the seasonal adjustment for each quarter.
(6 marks)

ii. An electrical bulb-making company runs a production line that contains 760 bulbs of the same wattage. These bulbs fail on a regular basis according to the following probability distribution:

Life (months)	Probability of Failure (P)
1	0.27
2	0.56
3	0.17

Required:
If the cost of replacing a bulb is N60, determine the following:

The life span (2 marks)
The average number of replacements in the period (1 mark)
The average monthly cost of replacing the bulbs. (1 mark)

Answer

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Tags: Forecasting, Moving Averages, Seasonal Adjustment
Level: Level 1

Topic: Operations Research
Series: MAY 2016

QTB – May 2016 – L1 – SB – Q6a – Data Collection Analysis

This question involves calculating moving averages and centered moving averages for quarterly sales data.

Question

The quarterly sales figures of company ABC Plc. for 3 years are as recorded below:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
Year 1	30	34	37	41
Year 2	45	49	54	57
Year 3	59	66	70	74

Required:
i. Calculate:

The moving averages.
(9 marks)

ii. The centered moving average for Quarter 3, Year 1.
(1 mark)

Answer

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Tags: Moving Averages, Seasonal Adjustment, Time series
Level: Level 1

Topic: Data Collection Analysis
Series: MAY 2016

MI – Nov 2023 – L1 – SB – Q3 – Forecasting Techniques

Calculation of moving averages, trends, and seasonal variations based on four years of historical sales data.

Question

The figures given below are four years’ historical sales data of a company.

Required:
Calculate the moving averages, trends, and seasonal variations.

Answer

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Tags: Forecasting, Moving Averages, Seasonal Variations, Trend Analysis
Level: Level 1

Topic: Forecasting Techniques
Series: NOV 2023

MI – May 2024 – L1 – SB – Q1 – Forecasting Techniques-Analysis, Moving Averages

Analyze a time series and describe two models for estimating seasonal variation.

Question

a. Describe how a time series can be analyzed. (10 Marks)

b. “There are TWO models used to estimate seasonal variation.” List and briefly describe the TWO models. (10 Marks)

Answer

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Tags: Additive model, Moving Averages, Proportional Model, Seasonal Variation, Time series
Level: Level 1

Topic: Forecasting Techniques-Analysis, Moving Averages
Series: MAY 2024

QT – May 2019 – L1 – Q5b – Forecasting

Compute 5-period moving averages, weighted moving averages, and comment on their suitability for forecasting

Question

The number of enquiries being made to a mail order business during a Monday to Friday working week is given as:

Week	Monday	Tuesday	Wednesday	Thursday	Friday
1	34	36	24	25	41
2	33	34	24	23	43
3	35	37	25	25	47

Required: i) Plot the data on a graph.
ii) Compute a 5-period moving average for the data.
iii) Compute a ‘weighted’ moving average for the data if the smoothing constant is $α = 0.5$ .
iv) Superimpose the graphs of (ii) and (iii) on your graph in (i) above.
v) Comment on the suitability of the two smoothing methods above. (16 marks)

Answer

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Tags: Data Plotting, Forecasting, Moving Averages, Time series, Weighted Moving Averages
Level: Level 1

Topic: Forecasting
Series: MAY 2019

QT – May 2019 – L1 – Q5a – Forecasting

Explain the concepts of moving averages and exponential smoothing in time series forecasting.

Question

The objective of smoothing methods is to smooth out the random variations due to irregular components of the time series and provide an overall impression of the pattern of movement in the data over time.

Required:
Explain the following smoothing methods:

i) Moving averages (2 marks)
ii) Exponential smoothing (2 marks)

Answer

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Tags: Exponential Smoothing, Forecasting, Moving Averages, Smoothing Methods, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2019

QT – May 2019 – L1 – Q1a – Forecasting

Calculate centered trend values using moving average, determine seasonal variations, adjust variations, and forecast future clients using a multiplicative model.

Question

The number of clients who consulted Tsoo Consult within a period of three years were recorded as follows:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
1	75	70	75	80
2	95	85	80	65
3	100	105	115	90

Required:
a) Assuming a 4 quarterly cycle, calculate the centred trend values for the data by moving average method. (4 marks)

b) Using (a) above and the multiplicative model, calculate the average seasonal variations. (5 marks)

c) Using (b) above, calculate the adjusted average seasonal variations for the data. (5 marks)

d) Using the trend and the adjusted average seasonal variation, forecast the number of clients for Year 4 based on the multiplicative model. (6 marks)

Answer

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Tags: Forecasting, Moving Averages, Multiplicative Model, Seasonal Variation, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2019

QT – May 2018 – L1 – Q4 – Forecasting

Calculate centered moving averages, seasonal variations, and forecast sales using the multiplicative model.

Question

a) The quarterly unit sales of electronic items of a retail company for the last three years are as follows:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
2013	100	115	70	210
2014	120	165	100	220
2015	150	195	120	270

Required:
i) Calculate a centered three-moving average of the unit sales. (3 marks)
ii) Calculate the trend using a centered four-quarterly moving average. (4 marks)
iii) Calculate the four seasonal variations using (ii) and the multiplicative model. (7 marks)
iv) Forecast the number of unit sales for the year 2016 using the multiplicative model. (4 marks)
v) Comment on your answer in (iv). (2 marks)

Answer

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Tags: Forecasting, Moving Averages, Seasonal Variations, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2018

QT – Nov 2018 – L1 – Q6b – Forecasting

Calculate the moving average, trend values, seasonal variation, and forecast membership.

Question

Membership of Pro Amalion, a network of professional volunteers, has grown over the years but in the months of the second quarter, there was always a decline. The table below shows membership records for a period of four years:

Year	1st Quarter	2nd Quarter	3rd Quarter	4th Quarter
Year 1	713	694	735	755
Year 2	767	733	766	780
Year 3	787	755	798	814
Year 4	816	790	826	843

Required:
i) Calculate the centered four-quarterly moving average of membership. (4 marks)
ii) Using a least squares trend equation based on (i) above, calculate the trend values. (5 marks)
iii) Using (ii) above, calculate the percentage seasonal variation and the average seasonal variation of membership. (5 marks)
iv) Determine the seasonally adjusted forecast of membership for each of the four quarters of Year 5. (4 marks)

Answer

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Tags: Forecasting, Least Squares, Membership Forecast, Moving Averages, Seasonal Variation, Time series
Level: Level 1

Topic: Forecasting
Series: NOV 2018

IMAC – MAR 2024 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis

Calculate daily variations using moving averages and explain interrelationships between material price and usage variances, and labor rate and efficiency variances.

Question

a) BB Importers Ltd has been importing electrical gadgets through the port of Takoradi over the past ten years. Management is aware that the business has been facing seasonal fluctuations but there is no scientific basis for the determination of such variations that can be used to predict future revenue. As a newly recruited Cost Accountant, you have been provided with some past daily sales performance over a three-week period. Details of the sales performance are shown below:

Sales	Monday	Tuesday	Wednesday	Thursday	Friday
Week 1	780	830	890	850	850
Week 2	880	930	990	950	950
Week 3	980	1030	1090	1050	1050

Required:
Using daily moving averages, calculate the daily variation for the company. (15 marks)

b) The reasons for variances might be connected, and two or more variances may arise from the same cause. For example, a favorable variance and an adverse variance might have the same cause.

Required:
Explain the interrelationships between:
i) Material price and usage variances (2.5 marks)
ii) Labor rate and efficiency variances (2.5 marks)

Answer

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Tags: Material Price Variance, Moving Averages, Sales Forecasting, Usage Variance
Level: Level 1

Topic: Forecasting, Standard Costing and Variance Analysis
Series: MAR 2024

IMAC – NOV 2023 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis

Determine the trend and seasonal variation in sales using moving averages and calculate factors for estimating direct material costs.

Question

a) A company operates from Monday to Friday. Sales data for the most recent three weeks as well as the moving total are as follows:

Day	Sales	Moving Total
Day 1	78
Day 2	83
Day 3	89	420
Day 4	85	430
Day 5	85	440
Day 6	88	450
Day 7	93	460
Day 8	99	470
Day 9	95	480
Day 10	95	490
Day 11	98	500
Day 12	103	510
Day 13	109	520
Day 14	105
Day 15	105

Required:
i) State the length of the cycle. (2 marks)
ii) Using the moving averages, establish the trend of the historical data above. (6 marks)
iii) Calculate the seasonal variation for each day of the week. (7 marks)

b) The value of variances as a control technique for management depends on the reliability and accuracy of the standard costs. If the standard costs are inaccurate, comparisons between actual cost and standard cost will have no meaning.

Required:
Explain TWO (2) factors to be considered by the purchasing department in estimating the direct material costs per unit of raw material. (5 marks)

Answer

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Tags: Direct Material Costs, Moving Averages, Sales Forecasting, Seasonal Variation
Level: Level 1

Topic: Forecasting, Standard Costing and Variance Analysis
Series: NOV 2023

Question Tag: Moving Averages

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QTB – May 2016 – L1 – SB – Q6b – Operations Research

This question involves calculating seasonal adjustments based on moving average analysis for sales data.

QTB – May 2016 – L1 – SB – Q6a – Data Collection Analysis

This question involves calculating moving averages and centered moving averages for quarterly sales data.

MI – Nov 2023 – L1 – SB – Q3 – Forecasting Techniques

Calculation of moving averages, trends, and seasonal variations based on four years of historical sales data.

MI – May 2024 – L1 – SB – Q1 – Forecasting Techniques-Analysis, Moving Averages

Analyze a time series and describe two models for estimating seasonal variation.

QT – May 2019 – L1 – Q5b – Forecasting

Compute 5-period moving averages, weighted moving averages, and comment on their suitability for forecasting

QT – May 2019 – L1 – Q5a – Forecasting

Explain the concepts of moving averages and exponential smoothing in time series forecasting.

QT – May 2019 – L1 – Q1a – Forecasting

Calculate centered trend values using moving average, determine seasonal variations, adjust variations, and forecast future clients using a multiplicative model.

QT – May 2018 – L1 – Q4 – Forecasting

Calculate centered moving averages, seasonal variations, and forecast sales using the multiplicative model.

QT – Nov 2018 – L1 – Q6b – Forecasting

Calculate the moving average, trend values, seasonal variation, and forecast membership.

IMAC – MAR 2024 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis

Calculate daily variations using moving averages and explain interrelationships between material price and usage variances, and labor rate and efficiency variances.

IMAC – NOV 2023 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis

Determine the trend and seasonal variation in sales using moving averages and calculate factors for estimating direct material costs.

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Question Tag: Moving Averages

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QTB – May 2016 – L1 – SB – Q6b – Operations Research

This question involves calculating seasonal adjustments based on moving average analysis for sales data.

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QTB – May 2016 – L1 – SB – Q6a – Data Collection Analysis

This question involves calculating moving averages and centered moving averages for quarterly sales data.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q6a – Data Collection Analysis"

MI – Nov 2023 – L1 – SB – Q3 – Forecasting Techniques

Calculation of moving averages, trends, and seasonal variations based on four years of historical sales data.

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MI – May 2024 – L1 – SB – Q1 – Forecasting Techniques-Analysis, Moving Averages

Analyze a time series and describe two models for estimating seasonal variation.

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QT – May 2019 – L1 – Q5b – Forecasting

Compute 5-period moving averages, weighted moving averages, and comment on their suitability for forecasting

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QT – May 2019 – L1 – Q5a – Forecasting

Explain the concepts of moving averages and exponential smoothing in time series forecasting.

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QT – May 2019 – L1 – Q1a – Forecasting

Calculate centered trend values using moving average, determine seasonal variations, adjust variations, and forecast future clients using a multiplicative model.

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QT – May 2018 – L1 – Q4 – Forecasting

Calculate centered moving averages, seasonal variations, and forecast sales using the multiplicative model.

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QT – Nov 2018 – L1 – Q6b – Forecasting

Calculate the moving average, trend values, seasonal variation, and forecast membership.

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IMAC – MAR 2024 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis

Calculate daily variations using moving averages and explain interrelationships between material price and usage variances, and labor rate and efficiency variances.

You're reporting an error for "IMAC – MAR 2024 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis"

IMAC – NOV 2023 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis

Determine the trend and seasonal variation in sales using moving averages and calculate factors for estimating direct material costs.

You're reporting an error for "IMAC – NOV 2023 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis"

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