Question

The snake undulation data o f Example 3.1 were measured in Hz, which has units of 1 / s (cycles per second). Often frequency measurements are expressed instead as angular velocity, which is measured in radians per second. To convert measurements from Hz to angular velocity (rad/s), multiply by 2π , where π = 3.14159.a. The sample mean undulation rate in the snake sample was 1.375 Hz. Calculate the sample mean in units o f angular velocity.b. The sample variance of undulation rate in the snake sample was 0.105 Hz2. Calculate the sample variance if the data were in units of angular velocity.c. The sample standard deviation of undulation rate in the snake sample was 0.324 Hz. Calculate the sample standard deviation in units of angular velocity. Provide the appropriate units with your answer.

Answer 1

(a) Sample mean is 8.639 rad/s

(b) Sample variance is 4.145 rad^2/s^2

(c) Sample standard deviation is 2.036 rad/s

Explanation:

(a) Sample mean = 1.375 Hz = 1.375×2π = 1.375×2×3.14159 = 8.639 rad/s

(b) Sample variance = 0.105 Hz^2 = 0.105×(2π)^2 = 0.105×4π^2 = 0.105×4×3.1415^2 = 4.145 rad^2/s^2

(c) Sample standard deviation = 0.324 Hz = 0.324×2π = 0.324×2×3.14159 = 2.036 rad/s