Chris_Killmer

Chris Killmer Stats 146 Welch’s fruit snack project October 26, 2023 Abstract : Introduction : My population of interest is all Welch’s mixed fruit, fruit snack pouches. I was curious about how the weight varies between pouches because I am often touching the bags to get a feel of which one has more gummies in it. On the back of the box, on the nutrient label, the weight in grams is displayed as 22.7 grams. I wanted to put that to the test, so I weighed 32 pouches and calculated the median, mean, and range of my 32-pouch sample. The quantitative variable I choose was the weight in grams, specifically to the tenth of a gram. I choose grams because that’s the same unit that is used on the nutrition facts, and I did not want to have any miscalculations if I wanted to convert from different measurement. I expect that all these pouches will weigh around the same as 22.7 grams. I expect no outliers either. I presume that the machines used to distribute the gummies per pouch are accurate to get near 22.7 grams.

Methods of Data Collection : To collect my data, I purchased a pack of 40 fruit snack pouches from Costco. I used simple random sampling to randomly pick out 32 out of the box of 40 pouches. I then weighed each one and recorded my data on a notebook. The scale I used was a food measuring scale created by American Weigh Scales (AWS). It has an accuracy of 0.1 grams. To calibrate the scale, I weighed a nickel which is supposed to weigh 5.0 grams, it weighed it as 5.1 so I’ll say my margin of error was +/- 0.1 gram. Any possible bias could be from the scales margin of error, and I only examined the weight of one box of fruit snacks. Results : The median was 22.8, the mean was 22.75, and the mode was 22.7. The lowest weight was 20.6 grams, and the highest weight was 24.5 grams. Nearly a 4-gram range! The standard deviation 0.8557. I calculated the IQR from 23.3-22.55 which gives me the IQR value of 0.75. Using the IQR I can determine if there are any outliers. 22.55 minus 1.5(0.8557) equals 21.3 rounded to the first decimal point. So, anything lower than 21.3 is an outlier. To calculate outliers that are bigger I would do 23.3 plus 1.5(0.8557) which equals 24.6, so anything over 24.6 is an outlier. I have three outliers, all on the lower side, 20.6, 21,2 and 21.3. Which means the histogram is skewed right. Outliers may be present because the machines or people used to evenly distribute the gummies to pouches are not going to be precise every time. It also could be a measurement error on my part, with a 0.1 margin of error.

My source of data was my scale which was a food measuring scale created by American Weigh Scales (AWS). The scale has an accuracy to the tenth of a gram, with a margin of error of 0.1. And of course, the 32 pouches I used for my data I got from Costco. Raw data: Calculations: TI-84 Calculator entry: Stat > Edit> enter values into L1. 1 Variable Stat Calculations: TI-84 Calculator entry: Stat > Calc > 1: 1-Var Stats > L1, calculate. X-bar: 22.753125 Sx: 0.8557148964 N: 32 minX: 20.6 Q1: 22.55 Med: 22.8 Q3: 23.3 Max: 24.5 Excel created the histogram and dot plot, as well as the two data charts. Sample Number Weight in Grams 1 20.6 2 22.6 3 22.7 4 22.7 5 21.3 6 22.7 7 23 8 23.2 9 23 10 23.2 11 24.5 12 23.6 13 23.6 14 21.9 15 21.5 16 23 17 22.5 18 23.2 19 23.4 20 22.9 21 23.3 22 23.7 23 23.5 24 23.3 25 22.7 26 22.1 27 22.7 28 22.6 29 22.7 30 23.8 31 21.2 32 21.4