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West Deptford High *

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290

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Marketing

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May 31, 2024

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pdf

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Uploaded by MajorTank11918

DESCRIBING DISTRIBUTIONS 1. A student measured the lifespans, in hours, of 10 batteries of Brand X and 10 batteries of Brand Y. The results are summarized in the dot plots. Part A: Describe the shape of the distribution in each dot plot. (4 points) Brand X is a symmetric distribution and Brand Y is positively skewed . Part B: Use the shape of the dot plot for Brand X to predict how the mean and median lifespans for that brand will compare. Will one be greater than the other, or will they be about equal? Then do the same for Brand Y. Explain your reasoning. (3 points) The mean and median have the same value for symmetric distribution while the mean is greater than the median for positively skewed distribution. Part C: Calculate the mean and median lifespans for Brand X and Brand Y. Are they consistent with your predictions? (4 points) X mean is 110 and median is 110, while Y is mean 130 and median 120, which are consistent with my predictions. Part D: What is the range for each brand? What does this tell you about the lifespans of these two brands? (4 points) Y range is 50 and X range is 40 so they are close in lifespan. Part E: Considering the data, which brand of battery should you purchase? Why? (3 points) Brand Y because it overall has a longer lifespan. COMPARATIVE BOX PLOTS 2. A gymnastics team has recently competed in three events. Each member of the team can score up to 10 points per event. The results of the first two events are represented in the box plots.

Part A: Use the five-number summary below to make a box plot for the scores on the third event, the balance beam. ( 5 points : 1 point for each part of the five-number summary being used appropriately) Minimum = 4 Lower quartile = 4.75 Median = 6 Upper quartile = 7.25 Maximum = 8 Part B: On which of the three events did the team tend to have the lowest scores? Explain. (3 points) The 3rd event because, while it shared the lowest minimum with uneven bars at a score of 4, the balance beam had the lowest maximum out of all three as well. Part C: Which two pieces of statistical information are most helpful in comparing two of the box plots? (2 points) The median and the IQR. Part D: What is the median value for the vault? (3 points) 8.50 Part E: Which event had the greatest range? What does that tell you about the scores on that event? (2 points) The uneven bars, the maximum was the highest out of all three with a 10. The median, 1st quartile and 3rd quartile all together had a higher placing despite the minimum outlier being 4. Part F: Which event had scores with the greatest IQR? Explain. (3 points) The balance beam because the IQR is 2.25 while the other two are about 1.75. TRANSFORMING DATA 3. Will is training for the upcoming football season. In a typical week he spends the following amounts of time training each day: 30, 45, 45, 15, 30, 30, and 0 minutes. Part A: What are the mean and median of his training times (rounded to the nearest whole number)? (2 points) Mean of training times: 28 Median of training times: 30

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