Statistical Analysis of Precision in Washer Drop Experiments

Statistical Analysis of Precision in Washer Drop Experiments: A Comparative Study of 20 and 10 Trials Abstract This report presents a statistical analysis of a washer drop experiment conducted in two phases: 20 trials and 10 trials.Assessing the precision in the location of each drop and the accuracy of the experimenter's aim.Using mean, standard deviation, and t-value calculations, the study compares the consistency of the two trial sets. Introduction This Lab report analyses a washer drop experiment conducted in two phases: 20 trials and 10 trials. We are calculating and comparing key statistical measures - mean and standard deviation - for both the x and y data across these trials. We aim to understand the consistency and precision in the washer drop locations by analysing these datasets. Methods and Procedures :

Place grid paper on a book or stack of papers to reduce washer bounce. Mark an intersection near the centre as the target and origin of the coordinate system. Position the washer on the fingertip, aligning it above the marked point. Quickly pull the finger down After each drop, trace the inner edge of the washer on the paper. Repeat this process for a total of 20 drops. Use a second piece of paper for another set of trials, repeating the process for 10 washer drops. Determine and mark the approximate centre of each traced circle. On each piece of graph paper, create a table listing the x and y locations of each circle's centre relative to the marked target, counting grid divisions as measurements. Calculate mean, standard deviation, and standard deviation of the mean for x and y data of the 20-point dataset. Compute only the mean for the 10-point dataset. Determine the difference between the means of the two datasets and express it as a multiple of the standard deviation from the first dataset. and express it as a way to drop the washer, minimising bounce or movement upon landing. Result Graphs unit X axis : 1 cm-1 unit Y axis : 1 cm - 1 unit

2. Calculate the mean value for the x and y data for the set of 20 trials (×20, y20). Show your work.

3. Calculate the standard deviation for x and y data for the set of 20 trials (ax, oy). Show your work.

Data Point x Value Squared Deviation (x) y Value Squared Deviation (y) 6 -1.0 1.6770 -1.6 4.2025 7 -1.0 1.6770 -1.1 2.4025 8 1.1 0.6480 1.1 0.4225 9 0.2 0.0090 0.4 0.0025 10 0.7 0.1640 2.0 2.4025 11 1.3 1.0100 1.6 1.3225 12 1.0 0.4970 0.4 0.0025 13 -0.5 0.6320 1.0 0.3025 14 -0.5 0.6320 0.3 0.0225 15 0.6 0.0930 0.4 0.0025 16 1.7 1.9740 0.8 0.1225 17 0.5 0.0420 1.5 1.1025 18 0.5 0.0420 0.0 0.2025 19 0.0 0.0870 0.0 0.2025 20 1.1 0.6480 1.2 0.5625 Sum= 10.5685 Sum= 15.37

4. Estimate the standard deviation of the mean for the x and y data for the set of 20 trials (6x, 8у). Show your work.

6. Calculate the number of standard deviations of the mean between the mean values of the two data sets. This is known as a t value/score. T_score = Mean1−Mean2/ Std Dev of Mean

.7 Respond to the following questions/instructions using complete sentences: (a) What is the precision with which you can measure each individual washer drop location? Explain your answer. The precision of each individual washer drop can be measured is its standard deviation. The standard deviation help show the spread of where the washer landed around the mean. For the 20- point dataset, the standard deviation for x (σx20) is approximately 0.7458, and for y (σy20) (b) What is the precision of your aim? Explain your answer.

Percentages can be misleading and misinterpreted due to how small of measurement we are using in this experiment.