Question

name jack hayden statistics chapter 4: mooseburgers and mctofu here are the weekly payrolls for two imaginary restaurants, mooseburgers and mctofu. 1. find the 5 - number summaries. statistic m - burgers mctofu min 110 100 q1 123 110 median 133.5 120 q3 144 132 max 160 360 2. create parallel boxplots. label your graph clearly. 3. write a few sentences comparing the distributions. 4. which restaurant pays the higher average salary? 5. why is the mean salary misleading? 6. at which restaurant would you rather work? give a sound statistical justification for your decision.

Explanation:

Step1: Calculate average for Mooseburgers

Sum of salaries = \(123 + 136+144 + 150+110+131+140+160+120+130\) = \(1344\). There are \(n = 10\) employees. Mean=\(\frac{1344}{10}=134.4\)

Step2: Calculate average for McTofu

Sum of salaries = \(110+115+130+100+120+146+117+129+360+132+107\) = \(1566\). There are \(n = 11\) employees. Mean=\(\frac{1566}{11}\approx142.36\)

Step3: Compare the averages

Since \(142.36>134.4\), McTofu has a higher average salary.

Step4: Analyze why mean is misleading

The mean for McTofu is affected by the out - lier value of \(360\). This high value pulls the mean upwards, making it not representative of the typical salary. Most employees in McTofu have salaries in the \(100 - 140\) range.

Step5: Make a decision

If considering the median, Mooseburgers has a median of \(133.5\) and McTofu has a median of \(120\). Also, the inter - quartile range (IQR) for Mooseburgers is \(Q3 - Q1=144 - 123 = 21\) and for McTofu is \(132-110 = 22\). Mooseburgers has a more consistent salary distribution around the median. So, if one wants a more consistent salary, Mooseburgers might be a better choice.

Answer:

1. The 5 - number summaries are as given in the table.
2. Parallel boxplots are as shown (boxplots are visual representations and cannot be fully re - created in text).
3. Mooseburgers has a more consistent salary distribution as its inter - quartile range is smaller. McTofu has a wider spread and an outlier which affects its overall distribution.
4. McTofu pays the higher average salary.
5. The mean salary for McTofu is misleading because of the outlier value of \(360\) which skews the mean upwards.
6. One might prefer to work at Mooseburgers because it has a more consistent salary distribution (smaller IQR) and a relatively high median salary compared to McTofu.