ICAP PRC-2 Quantitative Analysis for Business common mistakes
ICAP PRC-2 Quantitative Analysis for Business · Understand the traps and how to avoid them.
Computing a chain of percentage changes (e.g., a price rises 20% then falls 10%) by adding the percentages (+20% − 10% = +10%) instead of multiplying successive factors (1.20 × 0.90 = 1.08, a net +8%).
Percentages feel like additive quantities, and the candidate has practised single-step percentage questions but never a sequence where the base changes each time. Under time pressure the additive shortcut is the first thing that comes to mind.
What to do instead
Always convert each percentage change to a multiplier and multiply them in order; only the final product minus 1 is the net change. Drill three-step chains until you automatically write 1.2 × 0.9 rather than 20 − 10. For reverse questions (find the original given the final), divide by the product of multipliers rather than subtracting percentages.
Reporting the mean of grouped frequency data by averaging the class midpoints without weighting by frequency, or by using the midpoints of unequal-width classes as if the classes were equal.
Candidates memorise 'midpoint × frequency' but then reach for a plain average when the numbers look simple, and unequal class widths are easy to overlook because the table looks uniform at a glance.
What to do instead
Write the formula Σfx/Σf explicitly before substituting. Check class widths first; if they differ, use frequency density for histograms and be alert to whether the question needs a weighted mean. Sanity-check the answer lies inside the range of midpoints and close to where the data are concentrated.
Computing the median or quartiles of grouped data by taking the midpoint of the class containing the median rather than interpolating within the class.
The median class is correctly identified, then the candidate stops, because the interpolation formula feels like extra work and the midpoint is a plausible-looking number.
What to do instead
Use the interpolation formula: L + [(N/2 − cumulative frequency before the class)/class frequency] × class width (and analogous forms for Q1 and Q3). Practise until you can state the cumulative frequency just before the median class without hesitation. Remember the median of raw ungrouped data is a positional average, not an interpolated one.
Treating mutually exclusive events as independent, or independent events as mutually exclusive, when applying the addition and multiplication rules.
Both concepts are taught together as 'special rules', and the words look interchangeable. The candidate applies whichever formula was last revised rather than reasoning about whether events can co-occur.
What to do instead
State the test in words before choosing a formula: can both happen at once? If no, they are mutually exclusive and P(A and B) = 0. Does knowing one occurred change the other's probability? If no, they are independent and P(A and B) = P(A)P(B). Draw a two-way table or Venn diagram for every probability question until the distinction is automatic.
Applying a Laspeyres or Paasche index using the wrong year's quantities, or failing to distinguish a price index from a quantity index when the question gives both prices and quantities.
The formulas differ only in the subscript on q, and candidates memorise them as symbols without a story. They also assume 'base-weighted' always means the base year without checking which variable is being weighted.
What to do instead
Anchor the definitions verbally: Laspeyres uses base-period quantities (Σp₁q₀/Σp₀q₀), Paasche uses current-period quantities (Σp₁q₁/Σp₀q₁). Before calculating, label each column 'base' or 'current' and circle the quantity column you will use. Cross-check that a Paasche price index is generally lower than the corresponding Laspeyres index when prices and quantities move in opposite directions.
Computing a four-point moving average for a quarterly series and centring it wrongly, so the trend value is placed against the wrong quarter, or the seasonal index is averaged without adjusting for the residual.
Centring requires averaging two consecutive moving averages and aligning the result with the middle period; the bookkeeping is fiddly and candidates lose track of which quarter the trend belongs to.
What to do instead
Lay out a table with one row per quarter and columns for the raw value, the four-quarter total, the four-quarter average, the two-period centred average, and the ratio to trend. Place the centred average against the middle quarter of the eight quarters used. After averaging the ratios for each quarter, adjust the seasonal indices so they sum to 4 (or 400), dividing any discrepancy equally.
Interpreting a correlation coefficient as evidence of causation, or reporting r without checking linearity and outliers, then using the regression line to predict far outside the observed range.
The arithmetic of r and the regression equation is easy to execute mechanically, so candidates skip the diagnostic step and treat a high r as a licence to extrapolate confidently.
What to do instead
Before interpreting r, sketch the scatter and note any outlier or curved pattern; state that r measures only the strength of linear association and says nothing about cause. When predicting, check the x value lies within the data range and flag extrapolation explicitly. Remember r² is the proportion of variation explained and that the regression line passes through the means of x and y.
Mixing nominal and effective interest rates, or applying simple interest where compounding is implied, in present value, annuity and loan problems.
Candidates learn the annuity formula as a block and forget that i must be the rate per compounding period, so an annual nominal rate with monthly compounding is used directly.
What to do instead
Convert every rate to a per-period effective rate before substituting: i = nominal rate / number of periods per year, and n = years × periods per year. State whether the question asks for present value, future value, or the payment, and match the formula accordingly. For a nominal-versus-effective comparison, compute (1 + r/m)^m − 1 and check the effective rate exceeds the nominal one.
Choosing between maximin, maximax and expected monetary value by habit rather than by reading the decision criterion stated in the question, and ignoring the value of perfect information.
All three criteria use the same payoff table, and candidates who have drilled one method default to it even when the question specifies a risk-averse or risk-neutral decision maker.
What to do instead
Build the payoff table first, then write the criterion in the margin before computing: maximin takes the minimum of each row then the maximum of those; maximax takes the maximum of each row then the maximum; EMV weights each row by the stated probabilities and sums. For perfect information, compute the expected value with perfect information as Σ(probability × best payoff in each state) and subtract the best EMV.
Formulating a linear programme with an inequality pointing the wrong way for a minimum requirement, or solving graphically and testing the objective at the wrong corner of the feasible region.
Candidates translate 'at least 40 units of protein' into a ≤ constraint because the numbers are written left to right, and they evaluate corners without checking each satisfies every constraint.
What to do instead
Translate each constraint into a sentence with 'at least' or 'at most' before writing the symbol; 'at least' is ≥, 'at most' is ≤. After plotting, shade the feasible region and test one point to confirm the shading is correct. Evaluate the objective at every feasible corner, including intersection points, and state the optimal solution in the units the question asks for.