Final answer:
To average a large number of values like 1200 velocities, you should sum all the values and divide by the total count to get the average value. This process is straightforward for discrete data sets but can involve integrals for continuous data. Considering the proper significant figures is also important for precision.
Step-by-step explanation:
To average a large number of values, such as 1200 velocities, the correct method is to sum all values and divide by the count. This gives the mean or the average value. For example, if we are calculating the average speed of a car over a trip, we would use the formula:
average speed = total distance รท total time
When dealing with continuous distributions, such as velocities, the process can be more complex. It may involve using a probability distribution where you multiply the distribution function by the quantity to be averaged and integrate over all velocities. However, for discrete sets of data, like 1200 measured velocities, you would simply add them up and divide by 1200.
If you're plotting these velocities on a velocity vs. time graph, the average velocity can be visualized as the slope of the line (gradient) if the relationship is linear. The average can also be affected by outlier values; hence, sometimes considering the median or even trimming extreme values could be practical in certain contexts.
Choosing the highest value, only using the first 100 values, or taking the median does not yield the average velocity, though the median may give insight into the data's central tendency.
Significant figures should also be considered when reporting the average velocity to ensure that the precision of the calculation is clear.