Barry is currently obese and would like to lose weight. Barry is watching television and sees two different infomercials about weight loss products. The first infomercial is for a weight loss "supplement, called ICBINM (I Can't Believe It's Not Meth), the customer takes daily to "increase metabolism and energy". The infomercial for ICBINM shows 3 different verified customers who used the product and lost a lot of weight. The second infomercial is for a weight loss "program", called TNKD (The North Korean Diet), which tightly regulates which foods you eat and briefly "re-educates" (i.e., tortures) customers who break any diet rules, to reinforce the importance of sticking to the program. The infomercial for TNKD also shows 3 verified customers who followed the program and lost a lot of weight. Barry is interested in both of these products, but he wants more information before he decides whether to order either product. He calls up both companies and asks for any weight loss data they have for people who have used their product. Both companies indicate they have conducted research in which they had people use their product for 3 months and measured how much weight each person lost. Below is the data each company provides Barry. ICBINM: weight loss (in pounds) for 25 customers who used the product for 3 months TNKD: weight loss (in pounds) for 25 customers who followed the diet plan for 3 months 80 28 94 22 15 18 26 12 18 2 2 9 6 7 17 19 19 24 15 7 5 72 6 16 23 12 18 24 15 30 25 17 28 15 17 17 23 25 26 22 25 85 1 12 23 15 15 15 1) (5 points) What scale of measurement is the weight loss data (shown above) on? If you wanted to measure weight loss on a nominal scale of measurement, how would you do that? If you wanted to measure weight loss on an ordinal scale of measurement, how would you do that? 2) (15 points) Calculate the following information for each of the data sets given above: mean, median, standard deviation, minimum score, maximum score, 25h percentile score, 75 percentile score, interquartile range. Write a description of these two data sets based on your calculations. What do the mean and standard deviation tell you about the effectiveness of ICBINM and TNKD? 3) (5 points) Provide a group frequency distribution of each data set given above. 4) (5 points) Provide a histogram of the ICBINM data 5) (5 points) Provide a frequency polygon of the TNKD data. 6) (5 points) Create a box plot for each of the data sets. 7) (10 points) Would it be a better idea to use the median, rather than the mean, to summarize either (or both) of these data sets? Explain why or why not 8) (10 points) If Barry decides he is definitely going to purchase one of these two products to help him lose weight. Based on your analysis of the data for ICBINM and TNKD, which product is Barry better of using? Explain why you chose that product for Barry.
MEAN | Median | sd | min | max | 25th percentile | 75th percentile | Inter quartile range | |
ICBINM |
22.45833 |
16.5 |
24.34173 |
2 |
94 |
7 |
22.5 |
15.5 |
TKND |
22 |
20 |
14.88507 |
1 |
85 |
15 |
25 |
10 |
mean(ICBINM)=22.45833 which is greater than mean(TKND)=22 but standard deviation of ICBINM is greater than that of TKND hence TKND is showing consistancy among all customers. TKND is more effective.
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