ACCA MA · Chapter 2
Data analysis and statistical techniques MCQs with Answers
12 multiple-choice questions on Data analysis and statistical techniques for ACCA MA Management Accounting. Try each one before revealing the answer and explanation.
Practise this chapter interactivelyQuestion 1
A quality inspector chooses a random starting point from the first 20 items on a production list, then selects every 20th item after that. Which sampling method is being used?
- A) Simple random sampling
- B) Systematic sampling
- C) Stratified sampling
- D) Quota sampling
Show answer & explanation
Answer: B) Systematic sampling
Systematic sampling picks every nth item from a list after a random start. Simple random sampling gives every item an equal chance of being chosen independently, stratified sampling divides the population into groups first, and quota sampling is a non-random method.
Question 2
Which of the following sampling methods is a non-random sampling method?
- A) Stratified random sampling
- B) Quota sampling
- C) Simple random sampling
- D) Systematic sampling with a random start
Show answer & explanation
Answer: B) Quota sampling
In quota sampling the interviewer chooses who to include until a set number in each category has been reached, so not every item has a known chance of selection; it is a non-random method. Simple random sampling gives every item an equal chance of selection, stratified random sampling selects randomly within each stratum, and systematic sampling selects every nth item after a randomly chosen starting point, so chance determines which items are picked in all three.
Question 3
A cost index (base Year 1 = 100) stood at 160 in Year 4 and 184 in Year 6. What was the percentage increase in costs between Year 4 and Year 6?
- A) 24.0%
- B) 15.0%
- C) 13.0%
- D) 84.0%
Show answer & explanation
Answer: B) 15.0%
The percentage change is the change in the index divided by the starting index: (184 - 160) / 160 = 24 / 160 = 15.0%. The 24-point rise is not a percentage because the starting point is 160, not 100. Dividing by 184 gives 13.0%, which uses the wrong base.
Question 4
Prices and quantities for two items are as follows: Base year: Item X price $2, quantity 15; Item Y price $5, quantity 4 Current year: Item X price $3, quantity 8; Item Y price $6, quantity 6 What is the Laspeyres price index for the current year (base year = 100), to one decimal place?
- A) 130.4
- B) 135.0
- C) 138.0
- D) 120.0
Show answer & explanation
Answer: C) 138.0
A Laspeyres price index weights prices by base-year quantities: sum(p1 x q0) / sum(p0 x q0) x 100. Current prices x base quantities = (3 x 15) + (6 x 4) = 45 + 24 = 69. Base prices x base quantities = (2 x 15) + (5 x 4) = 30 + 20 = 50. Index = 69 / 50 x 100 = 138.0. Using current quantities would give the Paasche index of 60 / 46 x 100 = 130.4.
Question 5
The correlation coefficient between monthly output and total production cost has been calculated as 0.8. What proportion of the variation in total production cost is explained by variation in output?
- A) 80%
- B) 89%
- C) 36%
- D) 64%
Show answer & explanation
Answer: D) 64%
The proportion explained is the coefficient of determination, r squared. 0.8 x 0.8 = 0.64, so 64% of the variation in cost is explained by variation in output. The remaining 36% is due to other factors.
Question 6
A company has the following data for five periods, where x is output (000 units) and y is total cost ($000): Sum of x = 50, Sum of y = 400, Sum of xy = 4,300, Sum of x squared = 540, n = 5 Using linear regression (y = a + bx), what is the estimated total cost ($000) when output is 12,000 units?
- A) 95.0
- B) 90.0
- C) 96.0
- D) 67.5
Show answer & explanation
Answer: A) 95.0
b = (n x sum xy - sum x x sum y) / (n x sum x squared - (sum x) squared) = (5 x 4,300 - 50 x 400) / (5 x 540 - 50 x 50) = (21,500 - 20,000) / (2,700 - 2,500) = 1,500 / 200 = 7.5. a = (sum y - b x sum x) / n = (400 - 7.5 x 50) / 5 = 25 / 5 = 5. At x = 12: y = 5 + 7.5 x 12 = 95.0, i.e. $95,000.
Question 7
Which value of the correlation coefficient (r) indicates perfect negative correlation?
- A) 0
- B) -1
- C) +1
- D) -0.5
Show answer & explanation
Answer: B) -1
r ranges from -1 to +1. A value of -1 means all points lie exactly on a straight line sloping downwards (perfect negative correlation), +1 means perfect positive correlation, and 0 means no linear correlation.
Question 8
Quarterly sales trend is given by y = 200 + 5t, where t is the quarter number. Quarter 21 is a first quarter, which has a multiplicative seasonal index of 1.10. What is the forecast sales figure for quarter 21?
- A) 305.0
- B) 335.5
- C) 277.3
- D) 330.0
Show answer & explanation
Answer: B) 335.5
Trend for t = 21: 200 + (5 x 21) = 305. Under the multiplicative model the forecast = trend x seasonal index = 305 x 1.10 = 335.5. Dividing by 1.10 (277.3) would deseasonalise rather than forecast, and 330.0 uses t = 20 by mistake.
Question 9
In time series analysis, which component describes long-term, wave-like movements linked to the economic or business cycle over several years?
- A) Seasonal variations
- B) Random variations
- C) Cyclical variations
- D) The trend
Show answer & explanation
Answer: C) Cyclical variations
Cyclical variations are medium- to long-term swings caused by the business cycle and last several years. Seasonal variations repeat within a year, random variations are irregular one-off effects, and the trend is the underlying long-term direction.
Question 10
A project has the following possible outcomes: Profit $50,000 with probability 0.3 Profit $20,000 with probability 0.5 Loss $10,000 with probability 0.2 What is the expected value of the project?
- A) $27,000 profit
- B) $20,000 profit
- C) $25,000 profit
- D) $23,000 profit
Show answer & explanation
Answer: D) $23,000 profit
EV = sum of (outcome x probability) = (50,000 x 0.3) + (20,000 x 0.5) + (-10,000 x 0.2) = 15,000 + 10,000 - 2,000 = $23,000. Treating the loss as a profit gives $27,000, and leaving it out gives $25,000.
Question 11
Which of the following is a limitation of using expected values for decision-making?
- A) Expected values cannot be calculated when some outcomes are losses
- B) Expected values ignore the size of each possible outcome
- C) The expected value may not be one of the possible outcomes and is less meaningful for a one-off decision
- D) Expected values can only be used when all outcomes are equally likely
Show answer & explanation
Answer: C) The expected value may not be one of the possible outcomes and is less meaningful for a one-off decision
An expected value is a long-run average, so it is most useful for decisions that are repeated many times. For a one-off decision the actual result will be one of the individual outcomes, which may differ greatly from the EV. EVs also ignore risk attitude. They can include losses and they do weight the size of each outcome by its probability.
Question 12
Cell B5 of a spreadsheet contains the formula =B2*(1+$C$1). If this cell is copied to cell C5, what formula will C5 contain?
- A) =C2*(1+$C$1)
- B) =C2*(1+$D$1)
- C) =B2*(1+$C$1)
- D) =C2*(1+C1)
Show answer & explanation
Answer: A) =C2*(1+$C$1)
B2 is a relative reference, so when the formula is copied one column to the right it becomes C2. $C$1 is an absolute reference (both column and row are fixed with $ signs), so it does not change. The copied formula is therefore =C2*(1+$C$1).