Let's break down the questions and work through the answers one by one using the data presented for Restaurant #1 and Restaurant #2:

1. How many tips were recorded from Restaurant #2?

• In the table for Restaurant #2, the value under "N" is the number of observations (tips). For Restaurant #2, it says 152.

Answer:

• 152 tips were recorded from Restaurant #2.

2. What is the minimum a tip could be on a meal in Restaurant #1 and still be more than 75% of all the tips left at that restaurant that week?

• The third quartile (Q3) tells us the value below which 75% of the data lies. For Restaurant #1, the third quartile (Q3) is 6.59. This means that 75% of the tips were less than or equal to 6.59.

Answer:

• A tip could be 6.59 to be more than 75% of all the tips left at Restaurant #1.

3. The dataset for Restaurant #1 has a quartile of $6.59. Explain what this means in terms of the tips on the 191 meals in the dataset.

• This means that 75% of the tips for the 191 meals in Restaurant #1 were less than or equal to 6.59, and the remaining 25% of the tips were greater than 6.59.

Answer:

• 75% of the 191 tips left at Restaurant #1 were less than or equal to $6.59.

4. What would happen to the mean of the dataset for Restaurant #2 if an additional tip, greater than the maximum, was added to the dataset? Explain or justify your answer.

• The mean is the average of all tips, and if we add a tip greater than the current maximum of 6.47 (Restaurant #2), the total sum of tips would increase while the number of tips would increase by 1. Since the new tip is higher than the current maximum, the mean would increase.

Answer:

• The mean for Restaurant #2 would increase if a new tip greater than 6.47 is added to the dataset.

5. What would happen to the standard deviation of the dataset for Restaurant #1 if an additional tip, less than the minimum, was added to the dataset? Explain or justify your answer.

• The standard deviation measures the spread of data around the mean. If a tip lower than the current minimum (0.33) is added, it would increase the spread of the data, making the standard deviation larger.

Answer:

• The standard deviation for Restaurant #1 would increase if a tip less than 0.33 was added to the dataset.

Let me know if you'd like to go into more detail on any of these answers.

Relative Questions:

1. What is the median tip amount for Restaurant #1 and what does it tell us?
2. How does the variability in tips compare between Restaurant #1 and Restaurant #2?
3. If an outlier tip was recorded, how would it affect the interquartile range (IQR) in either restaurant?
4. Could the shape of the distribution affect the mean or median more significantly? Why?
5. How could adding more tips below the median influence the standard deviation?

Tip:

Always check how the maximum or minimum values affect the mean and standard deviation when adding new data points.