Average decadal growth rate (%) of population is :
2015
Average decadal growth rate (%) of population is :
Answer: B. ~ 9.82% — CONCEPTA decadal growth rate is the percentage by which a quantity increases over one ten-year interval, measured against the value at the START of that…
- A.
~ 12.21%
- B.
~ 9.82%
- C.
~ 6.73%
- D.
~ 5%
Show answer & explanation
Correct answer: B
CONCEPT
A decadal growth rate is the percentage by which a quantity increases over one ten-year interval, measured against the value at the START of that interval: r = (Pend − Pstart) / Pstart × 100. Each decade therefore has its own base year, and that base changes from one decade to the next.
When several consecutive decades are given, the average decadal growth rate is the arithmetic mean of those individual decadal rates: r̄ = (r1 + r2 + … + rn) / n, where n is the number of decades — not the total rise divided by the number of decades.
APPLICATION
The table lists seven population figures spaced ten years apart, so it spans six consecutive decades. Compute each decadal rate against the population at the start of that decade, keeping four decimal places so that intermediate rounding does not distort the final average:
Decade | Population (million) | Decadal growth rate |
|---|---|---|
1951 → 1961 | 20 → 21 | (21 − 20) / 20 × 100 = 5.0000% |
1961 → 1971 | 21 → 24 | (24 − 21) / 21 × 100 = 14.2857% |
1971 → 1981 | 24 → 27 | (27 − 24) / 24 × 100 = 12.5000% |
1981 → 1991 | 27 → 30 | (30 − 27) / 27 × 100 = 11.1111% |
1991 → 2001 | 30 → 32 | (32 − 30) / 30 × 100 = 6.6667% |
2001 → 2011 | 32 → 35 | (35 − 32) / 32 × 100 = 9.3750% |
Now average those six rates:
Add the six decadal rates: 5.0000 + 14.2857 + 12.5000 + 11.1111 + 6.6667 + 9.3750 = 58.9385.
Divide by the number of decades, n = 6: 58.9385 / 6 = 9.8231.
So the average decadal growth rate of the population is about 9.82%.
CROSS-CHECK
Check the same figure by compounding instead of averaging. The population rose from 20 million to 35 million over the six decades, a factor of 35 / 20 = 1.75. A single constant decadal rate r that reproduces this satisfies (1 + r)6 = 1.75, so r = 1.751/6 − 1 ≈ 0.0978, that is about 9.78% per decade. Note that this is NOT identical to the arithmetic mean of 9.8231%: the compounded (geometric) rate and the arithmetic mean of varying rates are two different averages, and when the individual rates differ the compounded rate is always the smaller of the two. What settles this question is that both averages sit far nearer to ~9.82% than to any other value on offer, so the choice does not turn on which averaging convention was intended.
COMMON PITFALLS
Measuring every decade against the 1951 base: the whole rise is (35 − 20) / 20 × 100 = 75%, and 75 / 6 = 12.5% per decade. That is wrong because each decade must be measured against its own starting population, which itself keeps growing.
Quoting a single decade: the 1951–1961 rise is 5%, but that is only one of the six intervals and cannot stand for the average of all of them.