My wife got one of those electronic activity trackers a few months ago and has been diligently walking every day since then. At the end of the day she sometimes reads off how many steps she walked, as measured by her activity tracker. I am always impressed at how many steps she racks up during the day through a combination of regular activity and scheduled walks.

There has been a lot written about the accuracy of electronic activity trackers. Personally, I don't worry about accuracy as long as the errors are in the 10% range. The purpose of the tools are to give people an idea of how much they are moving and to encourage them to get off the couch. Whether someone walked 4.2 miles or 3.8 isn't as important as the fact that she walked about 4 miles.

Because my wife's daily numbers seem so impressive, I decided to download some data from other people who use the same device. The device can be linked to a person's Twitter account and programmed to tweet a summary of the person's activity level each day. The Tweets all have a common hashtag and format, so it is easy to download a few hundred tweets and prepare them for data analysis. In an act of statistical voyeurism, I present a descriptive analysis of the activity level of 231 random people who use a particular brand of activity tracker, as reported by their tracker for Sunday, August 17, 2014. You can download the SAS program that analyzes these data.

Distribution of steps

The trackers records steps. The histogram at the left shows the distribution of the number of steps taken for the 231 subjects. (Click to enlarge.) A kernel density estimate is overlaid, and various quantiles are displayed in the inset. The histogram shows that about 25% of the people in the sample walked fewer than 4,000 steps, and about half of the people walked fewer than 7,100 steps. About a quarter of the people walked more than 11,600 steps, and the I-am-very-active award goes to those people who walked more than 18,000 steps—they are the upper 95th percentile of this sample.

The tail of the distribution falls off rapidly, which means that there is a low probability of finding someone who walks more than 30,000 steps per day. In other words, this is not a fat-tailed distribution. On the contrary, a person in the upper percentiles is working her tail off!

How many steps does it take to walk a mile?

The tracker also reports distance in miles. The basic device uses an algorithm to convert those steps into an approximate distances so, as they say, your distance may vary (nyuck-nyuck!). The device does not know your exact stride length.

The scatter plot to the left shows the relationship between distance and steps. For people who take many steps, there is substantial variation in the reported distance. Probably some of those people were running or jogging, which changes the length of the stride. The line indicates predicted distance for a given number of steps, as calculated by a robust regression algorithm.

These data can help to answer the question, "How many steps does it take to walk a mile?" Based on these data, it takes an average person 2,272 steps to walk a mile. Of course, shorter people will require more steps and taller people fewer, and there is the whole debate about how accurate these trackers are at estimating distance. Nevertheless, 2,272 steps is a good estimate for a mile. For a simpler number, you can estimate that 10,000 steps is about four miles.

These data also enable you to estimate the length of the average stride, which is 2.32 feet, or about 71 centimeters per step.

What do you think of these data? If you use a fitness tracking device, how many steps do you take each day? Leave a comment.