Abstract

The purpose of this experiment is to understand the difference between precision and accuracy. One person measured the length of a laboratory table with a 20cm wooden rod while another person measured the width of the same laboratory table with a separate 20cm wooden rod. This was repeated 30 times. Data was collected to find the mean, standard deviation, percent discrepancy, relative error, and the normal distribution. Later in the experiment, the actual value of the length and width of the laboratory table was measured with a measuring tape. With the data provided, the results conclude that the estimated values are precise and fell within at least one standard deviation of the mean on a normal bell-shaped distribution. Therefore, the results agree with the theoretical predictions within experimental uncertainties.

Procedure

Quickly record the length and width of the table 30 times by using a 20cm wooden rod. The standard deviation of the mean and the mean values of the length and width were calculated by using the Graphical Analysis program. The uncertainty in the measured mean values and the error of propagation in the area were calculated using certain equations. The same table was then measured with a measuring tape. Then the percent discrepancy is calculated for the estimated and measured area value. Then the relative error is calculated for the estimated area. One of the measured values is then recorded in a histogram to view the normal data distribution.

Results

Table 1: Estimated mean and standard deviation values | Mean Value | Standard Deviation (GA) | Length (cm) | 167.5 | 3.0256 | Width (cm) | 75.2 | 2.1399 |

Table 2: Measured values and standard deviation | Value | Uncertainty | Length (cm) | 182.7 | .1 | Width (cm) | 75.5 | .1 |

a) Number of measurements within 1 standard deviation from the mean: 24

b) Number of measurements within 2 standard deviations from the mean: 30

Data Analysis

Discussion

Our results show that our estimated values were precise, but not one hundred percent accurate. With a 12596 cm^2 estimated area value and a 13794 cm^2 measured value, there was an 8.6849% discrepancy between being precise and accurate. Our percent of errors were completely random and normally distributed because the measured value of the area fell within the estimated area results. Therefore, our data had at least a 68% chance of being within one standard deviation of the mean value.
Based on the relative error, the measurements of the area were precise because the relative error was .84860%. Since our percent discrepancy was less than 5-10%, our experimental results are considered to be precise. The histogram of our length (cm) values does resemble the normal bell-shape distribution. The percent of our data that falls within one standard deviation of the mean was 80%. The percent of our data that falls within two standard deviations of the mean was 100%. These two percentage values agree with the theoretical prediction. The standard deviation of the mean values presented that these values were precisely close to the mean. The standard deviation of the mean is calculated by taking the average of the original data, subtracting the