Index Number and Base Year DI Sets: 3 Reading Rules

DILR

A table of index numbers looks like a table of data, and that is the trap. The numbers do not say how much was sold or earned. They say how much more or less than a base year, and every question depends on remembering that.

Three reading rules make these sets manageable: know what the base is, compute change from the right year, and never compare two series by index alone. This guide takes each rule with a small example, and shows how to convert between index and real values when a question gives you one real figure.

What an Index Number Is

An index number expresses a quantity relative to a base. If the base year is 2020 and its index is 100, then an index of 132 in 2022 means the quantity is 32 percent higher than in 2020. An index of 90 would mean 10 percent lower. The index itself carries no unit, and no information about the size of the quantity.

Indexes are used to track prices, production, sales and many other things, because they let you compare series that have different units or sizes. A set might show an index of sales for a company and an index of costs, both starting at 100 in the same year, and ask which grew faster.

In a DI set, the table or chart is often accompanied by a note that gives the base. It may be small and easy to miss. A habit of looking for the base year before anything else is worth more than any formula in this topic.

Rule One: Find the Base Before You Read

Before you read a single value, find the base year and the base index, which is usually 100. Write it at the top of your rough sheet. Then note whether there is any real value attached, such as sales in the base year of 500 units.

Without the base, you cannot convert an index into a real quantity. With it, you can. If sales in 2020 were 500 units and the index in 2022 is 132, then sales in 2022 were 500 times 132 divided by 100, which is 660 units. That one step turns an abstract number into something you can compare.

Also check whether the base is the same for every series. Some sets use different base years for different series, and some report two indexes with different bases in one table. If the bases differ, any direct comparison of the index values is invalid.

Rule Two: Change Is Measured From the Earlier Year

The index shows change from the base, not from the previous year. So to find the change between two years that are not the base, compare their indexes with each other. The percentage change from year one to year two is (index two minus index one) divided by index one, times 100.

Take a sales index with base 2020 equal to 100. The indexes are 110 for 2021, 132 for 2022 and 121 for 2023. The change from 2021 to 2022 is 22 index points, and 22 divided by 110 is 20 percent. The change from 2022 to 2023 is minus 11, and 11 divided by 132 is about 8.3 percent fall.

Notice that the year over year changes are not obvious from the table, which only shows change from the base. The growth from 2020 to 2022 is 32 percent, but that does not mean 16 percent a year, and it does not mean the 2022 figure grew 32 percent over 2021. Each comparison needs its own calculation from the correct earlier year.

The same idea connects to other topics. Our guide on percentage change and CAGR traps in CAT DI covers the base errors in more detail, and you can practise percentages questions to speed up the arithmetic.

Question	How to compute	Example from the set
Change from base year	Index minus 100	2022 is 32 percent above 2020
Change between two other years	Difference divided by the earlier index	2021 to 2022 is 22 over 110, which is 20 percent
Real value in a year	Base value times index over 100	500 times 132 over 100 is 660 units
Fall in percent	Fall in index divided by the earlier index	11 over 132 is about 8.3 percent

Rule Three: Never Compare Series by Index Alone

Two series can both be indexed to 100 and still be wildly different in size. Suppose product A has an index of 120 in 2022 and product B has an index of 150, both based on 2020 equal to 100. B grew faster in percentage terms, 50 percent against 20 percent.

But which sold more? You cannot say from the index. If A sold 400 units in 2020 and B sold 200 units, then in 2022 A sold 480 units and B sold 300 units. A is still larger in absolute terms, though B grew faster. A question that asks which sold more needs the base values.

The rule is to keep two questions separate. Which grew faster is answered by the index. Which is larger is answered by the real values. Many wrong options in DI sets are built from confusing the two, so read the question carefully for the words faster, more and larger.

Rebasing to a New Year

Sometimes a question asks you to take a different year as the base. To rebase, divide every index by the index of the new base year and multiply by 100. The relationships stay the same. Only the reference point moves.

Using the same sales indexes, rebase to 2021 equal to 100. The 2021 index of 110 becomes 100. The 2022 index of 132 becomes 132 divided by 110 times 100, which is 120. The 2023 index of 121 becomes 110. Now the numbers read directly as change from 2021: 2022 is 20 percent above, and 2023 is 10 percent above.

Rebasing is a good way to answer several questions about one reference year. It also helps check a calculation. The 20 percent we found for 2021 to 2022 matches the rebased value of 120, which confirms it. If the two methods disagree, one of them has an arithmetic slip.

Combined Charts and Weighted Indexes

Index data often arrives as a line chart with several series, or as a table beside a bar chart of real values. In such sets, the real values give the base and the index gives the growth. Use both to answer questions that mix size and growth.

A weighted index is built from several items, with each item given a weight. The combined index is the weighted average of the item indexes. If a question gives weights, compute the weighted average, and do not take a simple average. This is the same trap as averaging percentages without weighting, which appears in many DI sets.

For sets that combine several displays, our guide on reading combo charts in CAT DI and the worked examples in three solved bar graph DI sets show how to read the pieces together.

A Mini Set to Try

Here is a mini set to test yourself. A company has a production index with base 2020 equal to 100, and the values are 104 in 2021, 130 in 2022 and 117 in 2023. Production in 2020 was 800 tonnes.

Question one: what was production in 2022? It is 800 times 130 over 100, which is 1,040 tonnes. Question two: what is the percentage change from 2021 to 2022? The difference is 26 index points, divided by 104, which is 25 percent. Question three: by what percent did production fall from 2022 to 2023? The fall is 13 points, divided by 130, which is 10 percent.

Question four: rebase to 2022 equal to 100. The 2023 value becomes 117 over 130 times 100, which is 90, so production fell 10 percent, matching question three. Question five: in which year was production above the base by the largest percent? That is 2022, at 30 percent above 2020.

Work through the set once on paper, and notice that every answer came from one of the three rules. That is what these sets reduce to once the base is clear.

A Practice Routine

Start with five short sets where you only practise the base step: write the base and the base value, and convert two indexes to real values. Then add the percentage change step, using two non-base years. Finally, add the comparison questions that mix size and growth.

Time the first read of each set. If you spend more than a couple of minutes before answering the first question, you are probably over reading. Look at the question first, then find only the numbers you need. Index sets reward selective reading.

A CAT study planner can place short DI sessions in your calendar, and you can talk to a CAT mentor if percentage change questions keep slowing you down. DILR set types vary from year to year, so treat this as one skill among several.