Rhythmic variance influences the speed but not the accuracy of complex averaging decisions

David Greatrex1, Sarah Hawkins2

  • 1Centre for Music and Science, Faculty of Music, University of Cambridge, CB3 9DP, Cambridge, United Kingdom. dgr@greatrexgrp.com.

Related Concept Videos

Harmonic Mean01:09

Harmonic Mean

The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
Take the example of the speed of a car, which is the measure of the rate of distance traveled. If the vehicle traverses the same distance back-and-forth, its average speed equals the total distance traveled divided by the total time taken. However, if the car moves with varying speeds, then the arithmetic mean is more skewed...
3.1K
Variability: Analysis01:11

Variability: Analysis

Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
The range is a simple measure of variability, indicating the difference between the highest and...
135
Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 
73.6K
Weighted Mean00:57

Weighted Mean

While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
5.0K
Standard Deviation of Calculated Results01:14

Standard Deviation of Calculated Results

Standard deviation measures the spread of data around the mean value. Many large data sets follow a Gaussian distribution, also known as a normal distribution. This distribution is bell-shaped curved, with the most frequently observed value (mean or central value) in the middle. The farther away from the central value, the greater the deviation from the central value, and the lower the frequency.
A broad Gaussian distribution curve has a wider standard deviation, representing a data set with...
5.9K
Average and Instantaneous Velocity Vectors01:12

Average and Instantaneous Velocity Vectors

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object is (its position) during its motion, but also how fast it’s moving. The speed at which an object is moving is given by the rate at which the position changes with time. For each position, a particular time is assigned. If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity v.
6.2K