Calculated means for ONS outputs

You asked

Many ONS statistics will be derived by calculating the mean of data points. Can you please tell me what type of mean is used in which sections of the ONS? Please let me know how the mean is calculated in each major group of ONS outputs, for example, retail sales, CPI, RPI, PPI, house prices etc?

We said

Thank you for your request.

The Producer Prices Index (PPI) and Service Producer Prices Index (SPPI) are calculated using the weighted sum of price relatives, where the weight is the share of expenditure in the base period (the Laspeyres formula). For more information please see PPI Methods and Guidance (section 5.2) and SPPI methods and guidance (section 3.2).

Below Stage 1 aggregation large and medium businesses may be asked to provide more than one price quote. In these cases the price quotes are combined using the arithmetic mean of price relatives (Carli) to produce an item index for a particular business. We are currently undertaking some exploratory analysis to understand the impact of moving to a Jevons formula. There are no plans at present to change to a Jevons formula.

The proportion of item indices in PPI which require Carli aggregation has decreased over time from approximately 90% in 2012 to approximately 65% in 2017. The proportion in SPPI is less than 5%.

The House Prices Index (HPI) is compiled using the geometric mean of price relatives (Jevons). For more information please see Development of a single official House Price Index (section 3.2). The Jevons indices are weighted together using transaction data from the latest complete year (section 3.3).

The Index of Private House Rental Prices (IPHRP) is calculated using the geometric mean of price relatives (Jevons) at the lowest level, and indices are combined using private housing rental expenditure shares. For more information see also the article Improvements to the Measurement of Owner Occupiers’ Housing Costs and Private Housing Rental Prices (sections 4.2.9 and 4.2.10). Note also that the IPHRP is used as the measure of price change for private rental properties in CPIH, CPI and RPI.

The detailed aggregation methods used to compile price quotes into item indices in the Consumer Prices Index including owner occupiers’ Housing costs (CPIH), CPI and the Retail Prices Index (RPI) are supplied in the attached download. These are summarised in Figure 10.3 of Paul Johnson’s UK Consumer Price Statistics: a Review. The item indices are combined using expenditure shares from two years prior to the current year, which have been price updated to the price reference period. This is described in more detail in the Consumer Prices Technical Manual (sections 2.4, 2.5 and 2.6).

The attached download was used in setting up the formula for RPIJ when it was introduced in 2012/2013. The table has been updated to remove old items and introduce new ones.

Note that the Retail Sales Index (RSI) is not a price index. Value measures are deflated using consumer price statistics and the resulting volume index is a Laspeyres. For more information see the Retail Sales Index QMI (section 6 – Chained Volume Measures).