What was the average decadal growth in the number of cars during 1961 - 2011 ?

Concept. The decadal growth of a quantity is always measured against that decade’s own starting value: growth % = (value at the end of the decade − value at the start of the decade) ÷ (value at the start of the decade) × 100. The average decadal growth across several decades is the arithmetic mean of those separate decade percentages: each percentage is worked out on its own base first, and only then are they added and divided by the number of decades.

Application. The "Cars, Jeeps, Taxis" column gives 3.1, 6.82, 11.60, 29.54, 70.58 and 191.23 lakh for 1961, 1971, 1981, 1991, 2001 and 2011. Those six readings define five successive decades, so five growth percentages are required.

1. 1961 → 1971: (6.82 − 3.1) ÷ 3.1 × 100 = 3.72 ÷ 3.1 × 100 = 120.00%

2. 1971 → 1981: (11.60 − 6.82) ÷ 6.82 × 100 = 4.78 ÷ 6.82 × 100 ≈ 70.09%

3. 1981 → 1991: (29.54 − 11.60) ÷ 11.60 × 100 = 17.94 ÷ 11.60 × 100 ≈ 154.66%

4. 1991 → 2001: (70.58 − 29.54) ÷ 29.54 × 100 = 41.04 ÷ 29.54 × 100 ≈ 138.93%

5. 2001 → 2011: (191.23 − 70.58) ÷ 70.58 × 100 = 120.65 ÷ 70.58 × 100 ≈ 170.94%

Adding the five decade rates: 120.00 + 70.09 + 154.66 + 138.93 + 170.94 = 654.62. Dividing by the five decades: 654.62 ÷ 5 = 130.92%, which rounds to about 131%.

Cross-check. Two independent tests support this figure. First, an arithmetic mean must lie between the smallest and the largest of the values averaged, and 130.92% does sit between 70.09% and 170.94%. Second, the tempting shortcut of taking the whole 1961–2011 change, (191.23 − 3.1) ÷ 3.1 × 100 ≈ 6068%, and dividing it by 5 yields about 1214% — far outside the range of any individual decade, which is exactly why the five decade percentages must be averaged rather than the two endpoint values.