Explaining the trimmed mean and weighted median

We produce two key measures of underlying inflation. These are the trimmed mean and the weighted median, these measures are also known as ‘core’ inflation.

Core inflation is important for the Reserve Bank of Australia, researchers and economists as they track medium-term inflation. This assists with inflation targeting and assessing the health of the Australian economy.

These inflation measures reduce the impact of irregular or temporary price changes created through events like cyclones Larry and Yasi destroying banana crops or changes in legislation that impact the price of goods and services purchased by households. This approach closely aligns the underlying measures with the rate of inflation experienced by average households.

Seasonally adjusted quarterly movements of the CPI are used to produce the trimmed mean and weighted median. Seasonally adjusted movements allow for inclusion of goods and services that have sudden irregular price changes.

Examples of seasonally adjusted items are:

• highly seasonal products (e.g. fruit)
• once yearly price changes (e.g. Educational fees)

When the CPI is significantly affected by temporary events the trimmed mean and weighted median are largely unaffected. This gives a better picture of the inflation trend over this period, without the impact of temporary shocks.

The chart below illustrates the impact of events on the CPI and by comparison the relative smoothness of the trimmed mean and weighted median. This is largely due to the removal of temporary or one-off impacts.

Annual percentage change of the CPI compared to the trimmed mean and weighted median.

Events that impacted on the CPI

Large temporary impacts:

• Damage from Cyclone Larry caused a 400 per cent rise in banana prices in mid-2006. This was followed by a sharp fall in banana prices as they returned to normal price levels in 2007. A similar event occurred again in 2011 as a result of Cyclone Yasi.
• A one-off event such as the introduction of the childcare rebate in 2007, saw childcare costs for households fall 33 per cent.
• The fall in price of financial services in 2008-09 due to the global financial crisis.
• Changes in world oil prices like in 2014-15 which resulted in a fall in automotive fuel prices by 22 per cent.

For both the trimmed mean and weighted median, the 87 expenditure classes are sorted from lowest to highest based on their seasonally adjusted quarterly percentage change and weighting on the CPI. Based on this, a distribution of cumulative weights by expenditure class is created.

Trimmed mean

The Trimmed mean is calculated by removing expenditure classes in the bottom 15 per cent and the top 85 per cent of the distribution, leaving a weighted average of the remaining 70 per cent.

Expenditure classes which cross the 15 per cent and 85 per cent thresholds are partially included using the component of their weight which falls within the 70 per cent trim.

Weighted median

The weighted median is the seasonally adjusted quarterly percentage change of the expenditure class at (or immediately over) the 50th percentile of the distribution. This can also be understood as 50 per cent trimmed mean or the middle value.

Discover a more detailed explanation of the calculations behind these measures.

Various measures of underlying inflation have been produced by the ABS and other organisations over the years. The Australian Treasury initially produced ‘exclusion-based’ measures, which were estimated back to 1971.

These measures used data from the CPI and removed certain products with volatile price change, such as fruit and vegetables, meat and seafood, and automotive fuel. The ABS now produces exclusion-based measures. The number and type of these measures has grown and changed to meet the needs of users

Since 1993, the Reserve Bank of Australia has targeted inflation of between 2 and 3 per cent over the course of the business cycle. Inflation-targeting increased the need to measure the medium-term inflationary trend. At this time the Reserve Bank began using underlying inflation measures in its analysis of the economy, these included:

• exclusion-based measures, such as those produced by the Treasury and the ABS
• measures derived from the CPI data, such as the trimmed mean and weighted median

In 2007, the ABS assumed responsibility for the calculation and publication of the trimmed mean and weighted median series’ developed by the Reserve Bank. These measures, and the exclusion-based measures, can be found on the CPI page.

In 2010, the ABS conducted a major review of the CPI. The review recommended a number of changes. One of these changes was the calculation of seasonally adjusted CPI estimates, which are a key input into the calculation of underlying inflation measures.

From September 2011, the number of seasonally adjusted goods and services increased from around 20 per cent of the weight of the CPI, to a little over 60 per cent. The changes enhanced the quality of the seasonally adjusted data, which in turn improved the trimmed mean and weighted median measures.

Following the review of the CPI, since 2011 the average annual CPI movement has been 2.0 per cent. In comparison, the average annual movements in the trimmed mean and weighted median are 2.1 per cent and 2.2 per cent respectively. The difference is largely due to the fall in automotive fuel prices in 2014-15, which was trimmed from the underlying inflation measures.

Australian Bureau of Statistics (ABS) 2010, Outcome of the 16th Series Australian Consumer Price Index Review, Dec 2010.

ABS 2011, Seasonal Adjustment of Consumer Price Indexes, Sep 2011.

Parliament of Australia 1997, Treasury's Underlying Rate of Inflation, Monthly Statistical Bulletin Feature Articles, November 1997.

Roberts, I. 2005, Underlying Inflation: Concepts, Measurement and Performance, Research Discussion Paper 2005-05, Reserve Bank of Australia.