What do the numbers seven, nine, 11, 25 and 150 have in common?

They may feel familiar since they frequently pop up in business articles. So if you said they're related to workplace distractions and getting work done — bingo! — you're right.

## The Numbers Game

The Magical Number Seven: is the number of digits that the average individual can maintain in short-term memory. Cognitive psychologist George Miller reached this conclusion in 1955. Based on this research, US phone numbers were purportedly limited to seven digits, so people could carry phone numbers around in their heads.

This finding has become accepted fact, with the original research paper being cited a whopping 22,000+ times.

Nine refers to the "9:1 mismatch between what innovators think consumers want and what consumers actually want." Popularized by MIT professor and coiner of Enterprise 2.0 Andrew McAfee, this number is based on work by Harvard economist John Gourville

While originally tied to economics, this number is now part of product design doctrine as the amount by which a new product needs to be better than the incumbent solution in order to succeed in the marketplace.

Eleven is the number of minutes that an average worker spends on a task before being interrupted and 25 is the average number of minutes the same worker takes to resume the task once interrupted. This conclusion was reached by information scientist Gloria Mark in 2005.

One hundred fifty is the number of people with whom one can maintain stable social relationships. Popularly called the Dunbar number, after anthropologist Robin Dunbar, this number was originally derived by measuring the size of a primate’s brain neocortex and noting the corresponding social group size of that primate’s species.

Based on research comparing different species, Dunbar extrapolated that the social group size of humans should be 150 individuals.

## What Else Do These Numbers Have in Common?

While the business press regularly cites these numbers, what you probably don’t know is that all of them were derived from research comprising incredibly small sample sizes. In other words, take them with a grain of salt.

How small were the sample sizes?

Miller based his magical number "7" on a collection of research projects, none of which exceeded several tens of subjects.

The 9x ratio is based on economic studies of the endowment effect in consumer buying preferences. The author of the definitive work on the subject is economist Richard Thaler who had this to say about the effect, “What evidence exists to support this hypothesis [of the endowment effect]? Unfortunately, there is little in the way of formal tests.”

While the Endowment Effect seems firmly established by a broad set of daily experiences, its magnitude appears to be situation-dependent; the number nine is more of a rule of thumb than anything else.

The 11 minute interruption time and 25 minute task recovery time is based on a study of just 24 people (seven managers, nine analysts and eight developers to be precise).

In fact, one of the limitations stated in the research was the generalizability of the results: “As we observed only one organization, we can only generalize our results to companies with similar characteristics: high pressure firms where many different tools are integral to work, and where people manage multiple activities.” Yet these numbers continue to be quoted as if they are a universal fact, including in an article published just last week.

Dunbar’s number 150 is based on a surprisingly miniscule sample size. How small? In Dunbar’s own words, “the samples were small, often just one or two specimens for each species, and covering only about 70 of the 200-odd species of living primates.”

These numbers may represent the truth, but when you consider how flimsy the evidence is for their basis, it is truly inconceivable that they remain unchallenged.

## Big Data to the Rescue

Using small samples sizes is nothing new. Scientists often carry out research using small sample sizes because sometimes it is impractical to work with larger groups. And so far that has been best practice. But in today’s age of big data, that situation is changing radically.

An alternative form of research is picking up steam. These studies analyze huge datasets and make inferences from large-scale, statistically-significant patterns. While these studies are not altogether new (see for example, a 2004 study that analyzed over a half a million Usenet messages to see how people deal with an overload of messages), a new reality is being created to finally analyze how we really work.

This new reality exists thanks to the recent availability of large data sets made possible by cheaper storage. A particularly fertile source of data is publicly-available cloud services that capture and store data from many individuals and organizations. Case in point, Facebook already has a Data Science team whose task it is "to conduct large-scale, quantitative research to gain deeper insights into how people interact with each other and with their world.’

But it’s not just Facebook. Coupled with the availability of affordable analytical tools, many organizations are hiring newly minted data scientists to launch research based on what is now being called computational social sciences.

The newfound ability to accurately capture and analyze how people use information technology is also providing exciting opportunities for designing the digital workplace of tomorrow.