175 years ago today, a small army of enumerators set out all across Scotland - and the rest of the UK - tasked with carrying out a population census. It wasn't the first national UK census - that was organised in 1801, with others in 1811, 1821 and 1831 - but it was the first to attempt to record every man, woman and child in the country. As such, it is an enormously important record set for family historians.
The purpose of the census was to provide accurate and detailed statistical information about the country to enhance government decisions. This was arguably an approach that had been pioneered by Sir John Sinclair with the Statistical Account of Scotland - a monumental work that introduced the word statistics into the English language.
It seems a fitting day, then, for us to have completed phase one of our Scottish surnames project. The idea is really quite simple - to investigate the frequency and geographical distribution of surnames in Scotland using, among others, census records. In our client and transcription work, we have built up a large database of surnames - over 8,500 so far - found in Scottish historical records. We want to know how common each of these surnames is in Scotland, and whether they are more common in any particular part of Scotland.
Phase 1 of our project - which is now complete - entailed counting the number of times each surname is found in each of Scotland's 33 historic counties, and in the four largest cities (Aberdeen, Dundee, Edinburgh and Glasgow). Even the data-gathering part of this phase was a major task - we conducted over 300,000 database queries before we could even begin crunching the numbers.
Having got the raw data, we then compared the number of instances of each surname  in each county with the total population of that county, giving the number of instances of each surname per 100,000 people in each county (the surname density). We then compared each county-frequency value with the equivalent figure for the whole of Scotland, to get an indication of relative surname density. 
The higher the relative surname density, the more common the surname is in that county compared to Scotland as a whole. Our working hypothesis is that the higher the maximum relative surname density for a particular surname, the more likely that surname is to have a geographic origin in that area. We will be looking to test that hypothesis using a selection of surnames with known geographic origins. 
A corollary to this initial hypothesis is that the lower the maximum relative surname density, the less likely the surname is to have a specific geographic origin. This appears to be borne out to some extent by the surnames with the lowest maximum relative surname density, shown in the table below
None of the top 9 surnames have a single origin, and the tenth - Frazer - may simply be a statistical artefact caused by the unusual spelling.
Several other interesting facts emerge from the initial results of this study.
 For the purposes of this study, we treated Mc- and Mac- surnames as identical.
 For example, there were 1580 Browns in Aberdeenshire in 1841. The total population of Aberdeenshire was 193,062. This means that the surname density for Brown in Aberdeenshire is
Surname density (Brown in Aberdeen) = (1580 / 193,062) * 100,000 = 818.39
There were 28,617 Browns in the whole of Scotland in 1841, out of a total population of 2,589,636. So the surname density for Brown in Scotland is
Surname density (Brown in Scotland) = (28,617/2,589,636) * 100,000 = 1105.06
So the relative surname density for Brown in Aberdeen is
Relative surname density (Brown in Aberdeenshire) = Surname density (Brown in Aberdeenshire) / Surname density (Brown in Scotland) = 818.39 / 1105.06 = 0.7406
A relative surname density less than 1 indicates that the surname is less common in that county than in Scotland as a whole. Likewise a relative surname density greater than 1 indicates that the surname is more common in that county than in Scotland as a whole.
 A complication that arises here is that surnames based on specific place names may have first arisen elsewhere. Take for instance the surname Carstairs. This derives from the barony of Carstairs in Lanarkshire, but the surname is most commonly found in Fife. This can be explained by two 13th-century clergymen, Peter de Castiltarris (i.e. "of Carstairs") and John de Castiltarris, who were granted stipends in Dunkeld in 1231 and north-east Fife a little later in the 13th century. The progenitor of the surname presumably came from Lanarkshire, but the surname itself arose in and spread from Fife. Although perhaps at first glance counter-intuitive, this is in fact logical: it wouldn't make sense to refer to John of Carstairs in Carstairs itself, but away from Carstairs, "of Carstairs" would serve as a useful identifier.
Genealogy and Family History - A mix of our news, curious and intriguing discoveries. Research hints and resources to grow your family tree in Scotland from our team.