Time series index numbers

This guide is one in a series on different aspects of statistical literacy. The others can be found in the House of Commons Library's Good Information Toolkit.

What are index numbers?

Index numbers are a way of simplifying data to help show differences in relative (percentage) terms.

The most common use of index numbers is to measure change over time. The underlying data is converted to an index where the base value is set normally set to 100. The index number for a specific point in time shows how much it differs from the base value in percentage terms. A value of 110 means it is 10% higher than the base value, a value of 90 means it is 10% less than the base value, and so on.

As index numbers only look at change and have no units of their own, they can be used to compare changes in multiple time series that are measured in different units. Multiple time series indices may be presented in the same chart or table to show how each series has changed in relative terms compared with their base values.

Multiple time series can be combined into a composite index such as the Consumer Prices Index (CPI). This is particularly useful when the underlying data cannot be added together and measured in a meaningful way, for instance because the series are measured in different units. Composite indices measure overall change across their component time series. This is only possible because of the simplifying process of indexation.

Occasionally, index numbers are used to help compare differences between groups. These could be geographical areas, sections of the population, different industries or other groups. Here the base value could be the average value across all groups or the value for a specific important group. This guide does not look at this type of indexation in detail.

Simple time series indices

The conventional format for a time series index is to have a base ‘year’ (it could be a day, month or average across a period of time) which is set to 100.

The index is constructed by dividing each value in the original series by the base ‘year’ and then multiplying by 100. An example is shown below.

Here 2020 is the base year. Each value in the original series is converted to an index value with the same calculation (here divide by 50 and multiply by 100). This retains the relative values of the series, but makes it easier to calculate percentage differences from the base year. For instance, the index value for 2024 is 140, which is 40% above the base year.

The process of indexation does not change the relative values or the ‘shape’ of a time series, as illustrated below. The shape of the lines in the two charts, one with absolute values (on the left) and the other with index numbers (on the right), are identical. It is only the absolute values – the numbers on the vertical axis – that have changed. The horizontal line at 100 in the index chart helps with making comparisons.

Source: DESNZ, Annual domestic energy bills (Table 2.3.1)

In general, any value X in the index is X% of the base ‘year’ value. This is not the percentage difference from the base year. To get the percentage difference you must subtract 100 from the index value:

• a value of 108 is 108% of the base ‘year’ value. 108 – 100 = 8, so the value is 8% more than the base ‘year’.
• a value of 92 is 92% of the base ‘year’ value. 92 – 100 = –8, so the value is 8% less than the base ‘year’.

Multiple data series can be converted to index values to help compare changes over time. This is particularly useful when the underlying data in the series are in different units. The process of indexation is the same as a single time series. Each index is constructed separately using its own base ‘year’.

The following chart shows index values of prices for different types of fuel. These prices are measured in different units so the underlying price series could not be included in a single chart; index numbers are used instead.

Sources: ONS series D7DU, D7DT, D7DW and D7DV

Multiple indices can also be used for series which are recorded in the same unit but with values that are so far apart that it is very difficult to compare how each has changed over time. The charts below illustrate this.

The first chart shows that transport by road was by far the most popular mode of transport. However, because it is so much more popular it is difficult to discern trends in rail or air travel on the same scale.

The second chart presents the trends for the three modes of transport in index form. It clearly shows the relative change for each mode of transport over this period, and which mode grew by more (compared with the base year) and over which time periods.

Source: DfT, Transport Statistics Great Britain (Table TSGB0101)

Effect of changes to base ‘years’

For a single simple time series index, the choice of base year has no effect on the relative values in the series, or its ‘shape’. Ideally, the index will use the ‘year’ which most users of the data will want to make comparisons with: setting the base year to 100 means that calculating percentages is easier. Often, the earliest point in a series will be used as the base ‘year’.

The effect of changing the base ‘year’ is greater when comparing multiple time series indices, especially where there are different trends in these series. This is illustrated in the charts below, which use different base years.

Source: DfT, Transport Statistics Great Britain (Table TSGB0101)

In this case, the change in the base year particularly affects air travel. This is because air travel grew much faster between 1990 and 2005 than between 2005 and 2020. The index values in the right-hand chart are:

• reduced by around 50% for air travel, reflecting growth in this sector between 1990 and 2005
• reduced by around 10% for road transport, reflecting growth in this sector between 2005 and 2020
• reduced by around 20% for rail travel, reflecting growth in this sector between 2005 and 2020

If all series you want to compare grow at similar rates between two points in time, then changing the base year between these times will have little effect on the relative values of the index series.

As a ‘consumer’ of these statistics, it is difficult to account for the effect of different base ‘years’. The best approach is to realise that there are instances where a different base ‘year’ could affect these comparisons, especially crossing points of, and gaps between, index lines on a chart.

It is also important to remember that index numbers are measures of change, not absolute values, when looking at charts of this type.

Composite time series indices

Composite indices combine multiple time series indices into a single index. Index numbers allow you to do this because they simplify their underlying data by focussing on changes in what they measure, not actual values and units. This means they can:

1. combine data which could not be summed in its original form, such as financial values, percentages and absolute numbers
2. measure change in something which cannot be directly measured or has no real meaning

Examples of composite indices include the CPI, the Natural History Museum’s Biodiversity Intactness Index (which measures how much of an area’s natural biodiversity is still left) or the UK’s biodiversity measure of the abundance of important animal species.

In essence, these composite measures are calculated by taking the weighted average of each component index. The value of the weights attached to each series can be a matter of value judgement, even if they are all given equal weights (as in the species abundance index).

Alternatively, some weights, such as those for financial data, can be calculated from the underlying data in an objective way. For instance, the weights used for the items in the CPI are calculated from their share of total expenditure in the ‘basket’ of goods included in this measure. The FTSE 100 uses the total market value of companies in the index to weight each component part.

Constructing composite indices can be extremely complicated. This might involve managing changes to their component parts, weights and base years. It might also need to deal with gaps in the underlying data or component parts which cover different time periods.

This guide does not look at such complexities. As a ‘consumer’ of statistics, the most important points to note about composite indices are that:

1. they focus on relative (percentage) changes in something
2. they have no units and can’t be added to or taken away from other values
3. their construction can involve elements of selection and/or value judgement so they could in theory be put together in another way which might give different results
4. points 1. and 2. are the same as for simple time series indices

Indices where the base year has little meaning

Well-known indices such as the CPI and FTSE 100 have values which are not meant to be compared directly with their base year. The main value of both indices is that, as composites, they combine multiple series of data and focus on their combined changes over time. This means that it is not possible to calculate percentage change over time by simply subtracting 100 from an index value; instead, change over time can only be calculated by working out the percentage change over a given period. Making comparisons with a base ‘year’ is not relevant in the same way that it is for many simple time series indices.

As of January 2026, the all-items CPI has a value of 139.4. This was 39.4% above its base year, which is the average for calendar year 2015, when the index was set to 100. However, the CPI is constructed to measure of year-on-year inflation. While the main use of the CPI is to calculate annual changes, it is simpler and clearer to keep a fixed base year rather than constantly changing it to the value from 12 months earlier. The Office for National Statistics publishes the 12-month change in CPI (inflation) as its main measure. The CPI itself is a background measure and useful for making comparisons over multiple years.

As of the end of April 2025, the CPI, the FTSE 100 is not intended for simple comparisons against a base year; it is used to calculate changes in the value of the companies it covers over different time periods, from different times in the same day to comparisons over many years.

As of the Start of March 2026, the FTSE 100 had a value of around 10,800. This was 9,800 points above its base, which is January 1984, when the index was set to 1,000. Like the CPI, the FTSE 100 is not intended for simple comparisons against a base year; it is used to calculate changes in the value of the companies it covers over different time periods, from different times in the same day to comparisons over many years.