Last month, I participated in a team building “Steppin Up Challenge” at work. We all had pedometers and logged our daily step count for 4 weeks. We also included our number of active minutes. There were 20 individual competitors who signed up for the event. For the next few posts I’m going to dig around the data and share some of the most interesting mathematical findings in this competition.

In total, the 19 people in our competition walked a total of 7.1 Million steps in 4 weeks. That’s roughly 13,383 steps per person per day. Wow! Now, we’ve probably all heard the recommendation that each person should take 10,000 steps per day. Why is that? The Centers for Disease Control and Prevention actually recommends getting 150 minutes of activity a week. For walkers, this amounts to about 10,000 steps per day, speed depending. So, on average, our competitors walked more than the suggested number of steps. Good job to us! But the next question is: did we achieve the minutes of exercise goal as well?

As it turns out, we were completing a weekly average of 607 minutes per week, or 10 hours per week. Definitely above the CDCs recommended values. So, how it is possible that we exceeded the goal of 10,000 steps per day by 30%, but we completely smashed the goal of 150 active minute per week by 400%?

This is probably because we were doing things that were active, but not step generating. Considering bicycling. A friend gave me some rough math from his bike commute; he found that he got about 450 “steps” on his pedometer for each mile he biked. This is less than a quarter of what he would get if he actually walked the mile. But, then we also need to consider that he is taking less time to travel that mile. So a pedestrian might spend 20 minutes to walk 2000 steps (=1 mile) while a bicyclist could spend 6 minutes biking the same distance to get 450 steps. If we normalize these, the pedestrian gets 100 steps per minute while the bicyclist gets 75 steps per minute. What about runners? If a runner can run an eight minute mile, they are running 2000 steps in 8 min. Thus a runner does approximately 250 steps per minute. *(edit: normal runners do not do 250 steps/min! Because a running stride is longer than a walking stride, it takes fewer steps to complete a mile. Perhaps a reasonable value would be 1500 steps/mile for an 8-10 minute mile. Thus an 8-10 minute mile could reasonably be between 170-180 steps/min.)*

So, what was the average steps per minute of our competitors? Are we more like runners or like walkers?

The average steps per active minute for the competitors over the 4 weeks of our challenge was 165.9 steps per minute of exercise. Wait a second- this is a value that is WAY above the steps/min we just computed for pedestrians and bicyclists! Why could that be? One option is that we are all runners. But I know I’m not a runner and did no running during the competition. I also know of many others in the same boat. We didn’t get high steps because we are avid runners. So why is that value so high?

Well, this is probably because there are a certain number of steps you take in a day that are definitely not associated with activity. All the steps you earn from walking back and forth from the refrigerator to get another diet orange Fanta don’t count towards your active minute total. But how do we decide what counts as activity and what does not? For this challenge, we decided to use the definition of active minutes that FitBit uses:

“Active Minutes” are awarded after 10 minutes of continuous moderate-to-intense activity. This includes walking at a brisk pace:

- E.g. You walk briskly to work for 11 minutes = 11 active minutes
- E.g. You walk briskly to get lunch in 5 minutes = 0 active minutes

So, we should be able to partition the steps into activity based steps and non-activity based steps. Like, there must be some average number of steps that everyone takes everyday that have nothing to do with the active exercise one does. This is a great question a basic a linear regression. With a linear regression, we are finding the best fit line of the data. We’ll get our regression results as an “m” and “b” as part of the y=mx + b equation for a line. The m tells us the what our average steps/active minute was. And the b is the y-intercept of the line– in this situation that is representative of the number of steps that we all took regardless of activity. For our data, b = 255487 steps. Take a look at the graph below for a scatterplot of the 19 competitors as well as the best fit line.

So if b = 255487 for the four weeks, this means we are, on average, taking 9124 steps per day, that are not exercise related. For reference, the average American supposedly walks between 300 and 3000 steps per day. Clearly there is a selection bias in our competitors! The people who signed up for the Steppin’ challenge have active lives even when they are not exercising. (Well except maybe contestant R, who appears to be a bit of an outlier).

Now let’s get back to the steps per minute computation. We want to see if our competitors are more like bikers (75 steps per minute) or runners (250 steps per minute). We originally computed 165.9 steps per day, but this included the 9124 steps we took everyday that had nothing to do with exercise. If we subtract that average from everyone and recompute the steps per active minute we get: 48.7 steps per active minute.

That feels really low! (Also note, the m from the regression gives us the slope between active minutes and steps. In this case, m = 49 steps per active minute. This is pretty close to our gross approximation of the 48.7 steps per minute.) As mentioned earlier, it’s probable that we were all doing exercise that doesn’t generate a lot of steps. But, we are even lower than biking? How?

Well, pedometers are very bad at measuring activity that doesn’t involve walking motions. And I know from anecdotal conversations that contestant M lifts a lot of weights. Weight lifting is definitely physical activity even though you get very few steps per minute. And personally, I do a lot of CorePower yoga. Yoga is definitely low step count. But if my sweat is any indication, it’s a good workout! Based on my experience, I get about 200 steps per hour of yoga. That’s only 3.3 steps per minute. If a bunch of contestants were all doing a few hours activity that involved only 200 steps/hour, then our global average will definitely drop below bicycling levels.

Based on this initial analysis, I’m concluding that this group does a lot of walking in their day to day lives. In contrast, the exercise completed by this group (on the whole) involves a lot of low stepping activities. However, there are some exceptions to this rule… But that’s a topic for next time!