Physics 50 Lab

Statistics Lab

Statistics Lab

Lab Instructor: Patricio Piedra

Lab Instructor: Patricio Piedra

Experiment I. Statistics

Background and Objective: Data collection is a complicated process because there are many factors that can introduce uncertainty, errors, and biases in the data. In order to minimize these uncertainties, care must be taken to make measurements as accurate as possible. Another way to make data more accurate is by having a large sample size with as many data points as possible. The objective of this lab is to see if there is a measurable difference between your reaction time measured by catching a falling ruler with your right hand, versus catching it with your left hand. The second objective is to get experience dealing with uncertainties and errors and how they affect the outcome of an experiment.

Measurements:

Data: Right hand distance (centimeters) | 20.12 | 9.53 | 27.44 | 16.62 | 16.73 | 23.25 | 20.34 | 21.72 | 20.13 | 21.82 | 21.73 | 12.56 | 24.13 | 17.52 | 27.93 | 19.52 | 24.33 | 22.65 | 15.73 | 24.52 | Average = 20.416 | Left hand distance (centimeters) | 29.22 | 24.51 | 25.73 | 15.82 | 6.34 | 23.25 | 29.44 | 25.32 | 21.43 | 23.32 | 17.42 | 20.46 | 18.27 | 26.43 | 20.33 | 19.43 | 17.63 | 13.14 | 12.63 | 16.34 | Average = 20.323 |

Figure 1. The above data was collected using a 30 cm ruler. 20 trials were done with each hand in order to minimize uncertainty and maximize accuracy by having a large sample size.

Figure 2: The histogram for the distance fallen when using the left hand. The specific intervals were chosen so that all the collected data could be included.

Figure 3: The histogram for the distance fallen when using the right hand. The specific intervals were chosen so that all the collected data could be included.

Average Distance for the right hand is 20.42 centimeters and average distance for the left hand is 20.32 centimeters.

Equations

1. The formula used for calculating the Standard deviation is as follows: x=The distance that the ruler has fallen. σy=<x2>-x2 The Standard deviation for the right hand is 4.64 centimeters.

The Standard deviation for the left hand is also 4.64 centimeters. 2. The formula used for calculating the average reaction time is as follows: t=Time y=average distance fallen in centimeters g=the gravitational constant in centimeters, which is 981 centimeters. t=2yg The average reaction time for the right hand is 0.204 seconds. The average reaction time for the left hand is 0.203 seconds. 3. The formula used for calculating the uncertainty of reaction time is as follows: y=average distance fallen in centimeters

g=the