We are certainly living longer than ever before. But within that statement lie a number of interesting stories neatly summarised by the Office of National Statistics (ONS) report on average life span in England and Wales, which came out around a year ago.

The first graph below has been constructed by first devising a rather artificial thing called a life table. This starts with 100,000 people at birth for each year and then, based on the probability of dying in the first year of life, works out how many are expected to survive to age 1. Of those, the probability of dying in the second year is applied to the number at year 1 in the table to work out the expected number of deaths during the second year. These are then deducted from the year 1 entry to arrive at the year 2 entry. And so on. Skip the next paragraph if that explanation is enough for you.

So, for example, taking the data from the England & Wales interim life tables 2009-11, we have 100,000 males at age 0, 99,508.2 at age 1 and 99,475.2 at age 2. This is because the probability of death for males in the first year of life over the 3 year period 2009 to 2011 was 0.004918, so 100,000 x 0.004918 = 491.8 expected deaths and 100,000 – 491.8 = 99,508.2 expected to be left in this imaginary population to celebrate their first birthdays. The probability of death in the second year of life was 0.000331 (notice this is much smaller, we will return to the significance of this later) so that the number of boys getting to blow two candles out on a cake is expected to be 99,508.2 – (0.000331 x 99,508.2) = 99,475.2. This table is nothing like real life of course, as we all move through time as we get older, so that our chance of death at age 20, say, would not be the same as the chance of a 20 year old dying 20 years earlier. However such a table does allow us to illustrate the patterns of deaths in any given year, and then compare these with other years.

The three measures used are based on the three averages you learned at school: the mean, median and mode.

The life expectancy at birth is a form of mean. The probability of reaching each age can be calculated by looking how many people you have at that age in your imaginary life table and dividing that number by the 100,000 you started with. Then each of these probabilities is multiplied by the age reached and then the probability of dying in that year (strictly the ONS life tables are constructed by taking the average probability for each year as the mid point between the start of the year and end of year probability, with a further adjustment in the first year when the probability of death is very much concentrated in the first 4 weeks). This can be shown to be same as all the entries (from year 1, year 2, year 3, etc) in the life table added up and divided by the 100,000 you started with.

The median is the age at which we expect half the population to have died. The mode is the age at which we see the highest number of deaths. The mode here has been adjusted in two further ways: the deaths below age 10 have been removed (otherwise it would have been 0 in a number of years and it is the old age mortality we are looking to compare) and it has also been smoothed to take out year on year fluctuations caused by wars and flu pandemics (again this would lead to modes in the 20s and 30s in some years, which are not the ages we are focused on).

There are many features to this graph, as set out in the ONS paper. The closing down of the gap between the mode on the one hand, and the median and life expectancy at birth on the other, is especially striking. This was mainly due to the massive improvement in survival rates in the first year in birth in particular. It also demonstrates that, contrary to what we might have believed about Victorian England, plenty of people were living into their 70s in the 1840s.

However I want to focus on the race to live longer between men and women because, armed with these three numbers (or six as we are looking at men and women separately) for each year, we can see that men and women have had a rather different journey since 1841.

As we can see the experience was fairly similar in the 1840s, although even then women lived 2 or 3 years longer on the mean and median measures than men. The modal age at death was more variable due to the relatively small numbers at advanced ages in the early years, but was between 25 and 30 years in excess of the median and life expectancy at birth due to the relatively high level of infant and child deaths at the time. The median and life expectancy then steadily advanced on the mode (interrupted by two downward spikes: in the mid 1840s a combined assault of typhus, flu and cholera, and a much larger one in 1919 from the flu pandemic).

In 1951, the female median age at death moved above the male modal age for the first time, marking the start of a 20 year period where life expectancy increases on all measures for women exceeded those of men. While the commonest age of death for men stayed in the mid 70s over this period, that for women increased from 79.5 to 82.5, leading to a peak difference in commonest age of death between men and women of 8.5 years in 1971. A graph of the differences in all three averages is shown below.

Since 1971 the tide has turned, with all six lines steadily, if very gradually, converging. In 2010 the male modal age at death finally crossed back over the female life expectancy at birth, and all three differences fell below 4 years for the first time since 1926. As the Longevity Science Advisory Panel’s second report points out, the average differences between life expectancy by gender at birth of 4.15 between 2005 and 2009 represent, in terms of the percentage of female life expectancy (5.1%), a return to the levels seen at the start of the journey in 1841. In 2010 this percentage fell to 4.7%. It has only fallen below that level four times since 1841, and not since 1857.

So we may be entering a new phase in the expected longevity differences between men and women. And, as the history shows us, those differences can change with surprising speed.