The Broken Series: Splicing Two Index Numbers Before Comparing
An Economics group in Dibrugarh is drafting a project on price change in Assam. They have the rural consumer price index on the old base, 2012 = 100: the 2015 reading is 128 and the 2023 reading is 245. From January 2024 a new series is published with base 2023 = 100, and for December 2025 the new series reads 118. A student writes in the draft: 'Prices rose by 245% between 2012 and 2023, and by a further 118% since 2023, so prices have more than tripled.' Another student wants a single table in which the December 2025 price level can be compared directly with 2015. The teacher must correct the draft without discouraging the group; the project carries 10 marks of internal assessment and is due in a week.
1. Identify the two errors in the student's sentence and restate the two facts correctly.
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Error one: reading an index number as a percentage change. An index of 245 on base 2012 = 100 means the 2023 price level is 2.45 times the 2012 level, so the rise is 145%, not 245%. The base year is the 100, and it must be subtracted before the number is called a percentage increase.
Error two: adding or chaining index numbers from two different bases as though they were the same scale. '118' is measured from 2023 = 100, so it describes the rise since 2023 only; it is not a continuation of the 2012 series and cannot be placed after the 245 figure as if the two sat on one ladder.
Correct statements: between 2012 and 2023 the index rose from 100 to 245, an increase of 145%. Between 2023 and December 2025 the new series rose from 100 to 118, an increase of 18% on the 2023 level. The corrected 'more than tripled' claim needs the splice computed, not asserted.
2. Express the December 2025 price level on the old base and calculate the percentage rise from 2015. Show the splicing factor.
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The two series overlap in 2023, which is what makes splicing possible. In 2023 the old series read 245 and the new series read 100, so one new-series point equals 245/100 = 2.45 old-series points. This ratio is the splicing factor.
December 2025 on the old base = 118 x 2.45 = 289.1.
Rise from 2015 to December 2025 = (289.1 - 128)/128 x 100 = 161.1/128 x 100 = 125.9%, approximately 126%.
So the price level at the end of 2025 was about 2.89 times the 2012 level, and about 2.26 times the 2015 level. The student's instinct that prices roughly tripled is not absurd, but it happens to be right for the wrong reason; the defensible statement is the spliced one, with the factor shown so a reader can audit it. If the group prefers, they may alternatively rebase 2015 onto the 2023 scale (128/2.45 = 52.2) and present the whole table on base 2023 = 100. Both routes give the same percentage change, which is a useful check.
3. The group asks whether they may simply quote the two series side by side in one table. Advise them, including one caution about what an index does and does not measure.
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Side by side is acceptable only if the table carries two clearly separate base rows or columns, with the base year marked and the series named; the reader must never be invited to subtract a 2012-base number from a 2023-base number. Comparability is the test: a table is honest when any difference a reader could compute from it is meaningful. Where the two series use different item baskets or weights, even splicing rests on an assumption that the overlap year is measured consistently, so the note under the table should say which base was used and how the link was made.
Caution about interpretation: a consumer price index measures the change in the cost of a fixed basket. It is not a measure of inflation experienced by every household, since spending patterns differ, and a Laspeyres-type index with base-year weights tends to overstate the rise because it ignores substitution towards cheaper items. The project should therefore avoid the phrase 'prices rose by x%' without saying whose basket is being priced.