The District Growth Figure That Was Averaged Wrong
A district has four branches. Deposits (₹ crore) for 2022 and 2023 are: Branch A 600 → 540; Branch B 250 → 275; Branch C 100 → 130; Branch D 50 → 60. A management trainee reports: 'Branch-wise growth is A −10%, B +10%, C +30%, D +20%, so the district grew at the simple average of these, 12.5%, comfortably beating the 10% district target.' The district head is about to forward this to the regional office. You have ten minutes to check the numbers and tell her whether the district target was met, and where the real problem sits.
1. Is 12.5% the district's growth rate? Compute the correct figure and explain the discrepancy in one paragraph.
Read the worked answer
No. 12.5% is the unweighted mean of four percentages; it is not a growth rate of the district.
Correct method: aggregate the base and the terminal values, then take one ratio.
- Total 2022 = 600 + 250 + 100 + 50 = ₹1,000 crore
- Total 2023 = 540 + 275 + 130 + 60 = ₹1,005 crore
- Growth = 5 / 1000 = 0.5%
Why the two numbers diverge: an unweighted average gives Branch D (₹50 crore) the same voice as Branch A (₹600 crore). In reality Branch A is 60% of the district, and its −10% wipes out ₹60 crore - more than the combined gains of B (+25), C (+30) and D (+10), which total +₹65 crore but on much smaller bases. Averaging ratios ignores the denominators. A cross-check confirms this: the rupee contributions sum to −60 + 25 + 30 + 10 = +₹5 crore, exactly the 0.5% found above.
2. The district head wants a one-line verdict for the regional office and a one-line action point. Draft both, with reasoning.
Read the worked answer
Verdict: 'District deposits grew 0.5% in 2023 against a 10% target - a miss of 9.5 percentage points; the previously reported 12.5% is a simple average of branch percentages and overstates performance.'
Reasoning: the target is a district-level target, so it must be measured on district-level aggregates. Comparing 0.5% to 10% is the only like-for-like comparison.
Action point: 'Growth is a single-branch problem - Branch A, at 60% of district deposits, fell ₹60 crore; B, C and D together added only ₹65 crore. Recovery plan and review to be anchored on Branch A, with B/C/D growth maintained.'
Reasoning for choosing A: the rupee contribution decomposition (−60, +25, +30, +10) shows that no plausible improvement at C or D can offset A. A 10% swing at Branch A is worth ₹60 crore; a 10% swing at Branch D is worth ₹5 crore. Prioritise by weight, not by percentage ranking - the fastest-growing branch is almost never the biggest lever when the base is small.