How can you determine the mean and standard deviation on a polar histogram?

Hello,

I am currently trying to find mean and standard deviation of my data during cycling. Each partcipant has 30 revolutions of pedaling and I found the angles where the peak values occur in each revolution. For some variables, the angles are distributed from mid 300 degrees to 90 degrees, which will be cancelled out when you just take the mean. So, I was wondering if there is any way to calculate the mean without cancelling out. I have attached sample data and figure below:

load example
min(example)

ans = 0

max(example)

ans = 6.2832

polarhistogram(example,'BinWidth',deg2rad(10))
set(gca,'ThetaZeroLocation','top','ThetaDir','clockwise')

If you have any suggestions or insights, please let me know. Thank you.

[VBBV]

can you tell more what you mean by "which will be cancelled out when you just take the mean" ?

[Youngmin]

@VBBV Thank you for your comment. Of course, I can tell you more about it. As you can see in the example data above, the maximum peak angle is 6.283 rad but the minimum peak angle is 0 rad. Given that the data was obtained during 30 consecutive revolutions of pedaling, both can be considered the same pedal position where the pedals are located at the top. When you take the average values across all data, the mean value is ...

load example
mean(example)

ans = 1.5516

I do not think this mean value can accurately represent the data, as the actual mean value appears to be approximately 0.7 rad when angles greater than 6 rad are converted to negative angles (e.g., converting 6 rad to -0.2832 rad). So, I was wondering if there is any way to calculate the mean angle without the skewness of the data.

histogram(example,20)

[Walter Roberson]

load example
norm_angle = example;
mask = norm_angle > pi;
norm_angle(mask) = norm_angle(mask) - 2*pi;
mean_angle = mean(norm_angle);

mean(mean_angle)

ans = 0.7138

Answer 1

[Walter Roberson]

You have to do something like

norm_angle = Angles;
mask = norm_angle > 180;
norm_angle(mask) = norm_angle(mask) - 360;
mean_angle = mean(norm_angle);

[Youngmin]

@Walter Roberson Thank you for your response. Although it is possible to apply this code to this example, it may cause the same issue on other variables as other variables could have different ranges of the angle.