BA1: Information and statistics

Answer: B. Information is data that has been processed, organised or analysed so that it has meaning and value for a particular purpose. Raw data on its own (such as a list of figures) is not yet useful until it is interpreted. Data is not defined by being numerical, nor is information defined by being in words. And data is generally less directly useful than the information derived from it, which is the whole point of processing it.

Answer: D. Big data analytics is used to identify patterns and relationships within large, varied and fast-moving datasets — for example, analysing customer behaviour to target marketing and understand value. The other options are routine, structured accounting tasks handled by conventional systems. The distinctive value of big data lies in extracting insight from volume, variety and velocity of data, not in standard transaction recording or compliance reporting.

Answer: B. The correlation coefficient ranges from −1 to +1. The sign shows direction and the magnitude shows strength. A value of −0.9 is close to −1, indicating a strong negative (inverse) relationship: as one variable rises, the other tends to fall. A weak relationship would be near zero, no relationship would be zero, and a perfect positive relationship would be exactly +1. The negative sign here rules out any positive interpretation.

Answer: D. The coefficient of determination is the square of the correlation coefficient (r²) and measures the proportion of variation in one variable explained by the other. Here r² = 0.8² = 0.64, or 64%. The 80% answer uses r itself rather than r², a very common error. The 40% answer halves the figure incorrectly, and the 89% answer takes a square root rather than a square. Squaring the coefficient is the key step.

Answer: B. In the additive model the actual value is the sum of its components: Trend + Seasonal + Cyclical + Random. This model is appropriate when seasonal variations are roughly constant in absolute size regardless of the trend level. The multiplicative model, by contrast, multiplies the components and suits series where seasonal variation grows in proportion to the trend. Options C and D do not represent either recognised model.

Answer: A. A histogram shows the frequency distribution of a continuous variable, with the area of each bar representing frequency across class intervals. Displaying parts of a whole is the job of a pie chart. Tracking a single value over time suits a line graph. Showing geographic location calls for a map. Choosing the right chart for the data type is a basic but commonly tested skill.

Answer: B. Substituting x = 8 into the trend equation: y = 200 + (15 × 8) = 200 + 120 = 320. The 215 answer uses x = 1 instead of 8. The 335 answer uses x = 9. The 1,720 answer incorrectly multiplies the intercept by 8 before adding. The intercept (200) is added once; only the slope coefficient (15) is multiplied by the period number.

Answer: B. In the additive model, forecast actual value = trend + seasonal variation = 480 + (−30) = 450. The negative seasonal factor indicates the quarter typically falls below the trend, so it is subtracted. The 510 answer adds 30 instead of subtracting it. The 480 answer ignores the seasonal adjustment entirely. Getting the sign of the seasonal factor right is essential when applying the additive model. 460 does not arise from any consistent treatment of the trend and seasonal figures.

Answer: D. Time series forecasts extrapolate historical patterns, so they rest on the assumption that the trend and seasonal relationships seen in the past will persist. If conditions change — new competition, economic shocks, shifts in consumer behaviour — the forecast can quickly become unreliable, and accuracy generally falls the further ahead one forecasts. The other options misstate how forecasting works; forecasts are numerical and do not require specialist software.

Answer: B. Spearman's rank correlation coefficient is designed for ranked (ordinal) data, measuring how closely two sets of rankings agree. Pearson's coefficient is used for variables measured on a numerical scale. The coefficient of determination (r²) measures explained variation rather than testing ranked data, and an arithmetic mean is an average, not a correlation measure. Matching the technique to the type of data is the key point.

Answer: B. The coefficient of determination, which measures the proportion of variation explained, is the square of the correlation coefficient: 0.6² = 0.36, or 36%. The 60% answer uses the correlation coefficient itself rather than its square — the most common error. The 77% answer is the square root of 0.6, and the 30% answer halves the coefficient. The coefficient must be squared to obtain the explained proportion.

Answer: C. A three-period moving average is the mean of the three values: (40 + 46 + 52) ÷ 3 = 138 ÷ 3 = 46. Moving averages smooth out short-term fluctuations to reveal the underlying trend. The figure 138 is the total before dividing by the number of periods; 49 is the average of just the first and last values; and 52 is simply the latest value alone. The key step is dividing the sum by the number of periods.

Answer: B. Good information is, among other things, relevant to the decision in hand — it helps the user make or evaluate a choice. Other recognised qualities include being accurate, complete, timely, understandable and cost-effective. Deliberately incomplete information and information delivered too late to influence the decision both fail these tests, and excessive detail beyond the user's needs reduces, rather than improves, usefulness.

Answer: D. In a linear cost equation y = a + bx, the slope coefficient b is the variable cost per unit — here, total cost rises by £8 for each additional unit produced. The intercept a (£500) is the fixed cost, incurred even at zero output, so both the 'fixed cost' and the 'total cost when no units are produced' answers describe the £500 figure rather than the 8. The equation describes cost behaviour, not selling price.

Answer: D. In the multiplicative model, forecast actual value = trend × seasonal index = 200 × 1.15 = 230. A seasonal index above 1 indicates a period that runs above the trend (here, 15% above). The figure 201.15 adds the index instead of multiplying; 174 divides by the index rather than multiplying; and 215 adds 15 to the trend. In the multiplicative model the components are multiplied, unlike the additive model where they are added.

Answer: A. The arithmetic mean is the sum of the values divided by the number of values: (12 + 15 + 18 + 20 + 25) ÷ 5 = 90 ÷ 5 = 18. The value 90 is the total before dividing. The value 20 is the median (the middle value when ordered), not the mean. The mean uses every value and divides by the count, which distinguishes it from the median or mode. 16 does not use all five values; it is the average of only the first and fourth values (12 and 20).

Answer: B. The median is the middle value when the data are arranged in order. With five ordered values (4, 7, 9, 12, 20), the third value, 9, is the middle one. The value 10.4 is the arithmetic mean (52 ÷ 5), not the median. The values 12 and 20 are simply other items in the set. With an odd number of observations the median is the central value; with an even number it is the average of the two central values.

Answer: C. The standard deviation measures the spread of values around the mean; a higher value means the data are more widely dispersed. It says nothing directly about the size of the mean or the number of observations, and a large standard deviation does not imply any particular distribution shape. It is a measure of variability, useful for comparing the consistency or risk of different data sets.

Answer: D. The mode is the value that appears most often in a data set, and a set can have more than one mode or none at all. The middle ordered value is the median, the sum divided by the count is the mean, and the gap between highest and lowest is the range. The mode is particularly useful for categorical data, where an average or median may not be meaningful.

Answer: A. The range is the difference between the highest and lowest values: 30 − 8 = 22. It is the simplest measure of dispersion. The values 30 and 8 are the highest and lowest themselves, not the range, and 17.4 is the arithmetic mean of the set. Although easy to calculate, the range uses only the two extreme values and so can be distorted by a single outlier.

Answer: C. Probability = favourable outcomes ÷ total outcomes = 12 red ÷ 20 total = 0.60. The value 0.40 is the probability of selecting a blue bead (8 ÷ 20), and 1.50 (12 ÷ 8) wrongly divides reds by blues rather than by the total. A probability must lie between 0 and 1, which immediately rules out 1.50. The total number of possible outcomes is the correct denominator. 0.12 treats the count of 12 red beads as if it were a probability.

Answer: D. Expected value = Σ(probability × outcome) = (0.4 × £100) + (0.6 × £50) = £40 + £30 = £70. The figure £75 is the simple average of £100 and £50, ignoring the probabilities. £150 adds the two outcomes, and £60 misapplies the weights. Expected value weights each possible outcome by its probability, so the more likely £50 outcome pulls the result below the simple average.

Answer: A. For a normal distribution, about 68% of values fall within one standard deviation of the mean, roughly 95% within two, and about 99.7% within three. The figure 50% would be the proportion below the mean. The 95% and 99% figures correspond to two and three standard deviations respectively. These benchmarks of the normal curve are widely used to judge how typical or unusual a value is.

Answer: B. The weighted average is the sum of (value × weight) divided by the sum of the weights: [(10 × 3) + (20 × 2)] ÷ (3 + 2) = (30 + 40) ÷ 5 = 70 ÷ 5 = 14. The figure 15 is the simple unweighted average of 10 and 20, which ignores the weights. Because the value 10 carries the greater weight, the weighted average is pulled below the midpoint of 15. 16 swaps the weights: ((10 × 2) + (20 × 3)) ÷ 5 = 80 ÷ 5.

Answer: C. A cumulative frequency distribution adds up frequencies in order, so it directly shows how many observations fall below (or above) a given value and is the basis for finding medians and quartiles. The most common value is the mode, the mean requires a separate calculation, and correlation concerns the relationship between two variables. Accumulating frequencies answers 'how many up to this point' questions.

Answer: C. The interquartile range is the difference between the upper and lower quartiles, capturing the spread of the middle 50% of the data and so ignoring extreme values at either end. The most frequent value is the mode and the average is the mean; neither measures spread. The largest value alone is not a measure of dispersion. Because it excludes the extremes, the interquartile range is less distorted by outliers than the range.

Answer: B. Substituting x = 10: y = 1,200 + (50 × 10) = 1,200 + 500 = 1,700. The intercept 1,200 represents fixed cost and the slope 50 the variable cost per unit, so total cost is fixed cost plus variable cost for 10 units. The figure 1,250 adds only one unit's variable cost, and 6,200 incorrectly multiplies the intercept by 10. Only the slope is multiplied by the number of units. 2,200 adds £1,000 of variable cost, as if 20 units had been produced.

Answer: C. The coefficient of variation = standard deviation ÷ mean = 10 ÷ 50 = 0.20, or 20%. It expresses variability relative to the mean, allowing comparison of dispersion between data sets of different sizes. The figure 500% inverts the ratio (50 ÷ 10), and 5% misplaces the decimal. Dividing the standard deviation by the mean, then converting to a percentage, gives the relative measure of spread. 40% is double the correct ratio and does not follow from the figures.

Answer: A. Qualitative data describe a quality or category rather than a numerical measurement, and satisfaction ratings expressed in words are qualitative (specifically, ordinal categories). Continuous and discrete quantitative data are numerical — measured on a scale or counted in whole numbers respectively. Time series data are values recorded over successive time periods. Data expressed as descriptive categories rather than numbers are qualitative.

Answer: C. Deseasonalising, or seasonal adjustment, strips out recurring seasonal variation so that the underlying trend and any genuine changes can be seen more clearly — widely used in reporting figures such as unemployment or retail sales. Extrapolating means projecting beyond the data, correlating measures the relationship between variables, and compounding concerns interest. Adjusting for season is the technique that isolates the trend.