phys 223 lab 1 report

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Statistics

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Apr 3, 2024

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January 16, 2024 PHYS 223-02 Experiment 1 Jasmine Warren, Mia Hardy, Ella Dozer Introductions and Objectives The objective of this experiment was to create a histogram with normal distribution. To do this we first had to take the bag that had 25 dice in it and separate them into 5 groups of 5 dice. Then we had to roll each of the 5 groups 20 times so that we would end up with 100 rolls total. After each roll we had to take note of what the 5 dice read. And then we had to add up those 5 numbers, keeping track of all these numbers in the data table. After we had all the data, we had to take the 100 sums and make a histogram with the sums on the x-axis and the number of occurrences on the y-axis. The number of occurrences was how many times a certain sum showed up. Once the histogram was created, we had to adjust the bin number (the groups that encompassed each bar on the graph) to go up by one so you could more easily see the distribution of data. Data Sheets and Graphs

This table is the data collected from the experiment. Within each of the 5 groups of dice that were rolled 20 times each, the numbers that were rolled were noted and then added together for the sum. This graph shows the number of occurrences of each sum we calculated. This gives you a visual distribution of the data to determine if it is normal or not. Analysis With the data that was collected, the mean (average) can be calculated by taking the sum of all the sums and then dividing that by 100 (since we have 100 data points). Looking at the histogram, you can estimate the average by looking at where the peak is compared to the overall distribution. In a normal distribution the mean will be the same as the mode (the sum that occurred the most) which would be seen as the peak on the graph and should be somewhere near the middle of the distribution of data. The mode of my data is 15 or 16. The median(middle data point) isn’t exactly where the mode is

but my peak is close to where you would expect the mean/median to be so this is a normal distribution. Discussion For this experiment the data collection method was good about giving us the most random and ‘normal’ data. Without organizing the dice in any way and just rolling them freely, all 6 numbers have an equal chance of being rolled. Next was finding the sums of those 100 rolls. The lowest possible sum is 5 if you rolled all ones and the highest possible sum is 30 if you rolled all sixes. Creating the histogram with those sums was slightly difficult at first since I have a Mac and excel is set up very differently, but once I learned how to adjust the bins it was fine. I also noticed that to get a correct histogram I needed to have all 100 data points listed in a continuous column. The first time I had copied the five columns of sums over to the side still in separate columns. I realized this was incorrect because the mode of my data was showing that 14 or 15 showed up 5 times. Looking back at my data table I knew there were far more than that and had to rearrange so it showed up correctly. Knowing how to read and interpret the histogram was important in catching that mistake. Looking at the correct histogram, you can see that it is pretty close to a normal distribution. In a perfect world you would expect the Gaussian curve to rise and fall evenly with the peak(mode) being directly at the center of the spread of data (median) keeping in line with the average(mean). If we were to continue this experiment with more rolls and more data points, we would get closer and closer to that ideal normal distribution. The mean could be calculated, compared to the graph to see that it is accurate, and then you can visualize it so it makes sense.

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Conclusion The objective of this experiment was to create a histogram of normal distribution with data from a random experiment. We rolled the dice and got random data, adding the numbers to get our data points, and then plotted them on a histogram vs number of occurrences of those values. My histogram came out to be a normal distribution with the mean, median, and mode seemingly at around the same location. I learned how to create and interpret a histogram with a normal distribution.

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