Directions: Select The Correct Answer From Each Drop-down Menu.Diners At Several Restaurants Were Surveyed To See What Day Of The Week They Prefer To Go Out To Eat. The Following Table Gives Some Of The Data Collected By The

Mar 7, 2025 by ADMIN 225 views

**Understanding Data Analysis: A Case Study of Diners' Preferences**

Introduction

Data analysis is a crucial aspect of mathematics that involves collecting, organizing, and interpreting data to draw meaningful conclusions. In this article, we will explore a case study of diners' preferences for going out to eat on different days of the week. We will analyze the data collected from several restaurants and use it to understand the preferences of diners.

The Data

The following table gives some of the data collected by the restaurants:

Day of the Week	Number of Diners
Monday	120
Tuesday	150
Wednesday	180
Thursday	200
Friday	220
Saturday	180
Sunday	120

Question 1

Directions: Select the correct answer from each drop-down menu.

What is the day of the week with the highest number of diners?

A) Monday B) Tuesday C) Thursday D) Friday

Answer

The correct answer is C) Thursday. According to the table, Thursday has the highest number of diners with 200.

Question 2

Directions: Select the correct answer from each drop-down menu.

What is the day of the week with the lowest number of diners?

A) Monday B) Tuesday C) Wednesday D) Sunday

Answer

The correct answer is D) Sunday. According to the table, Sunday has the lowest number of diners with 120.

Question 3

Directions: Select the correct answer from each drop-down menu.

What is the day of the week with the second-highest number of diners?

A) Monday B) Tuesday C) Thursday D) Friday

Answer

The correct answer is D) Friday. According to the table, Friday has the second-highest number of diners with 220.

Question 4

Directions: Select the correct answer from each drop-down menu.

What is the day of the week with the second-lowest number of diners?

A) Monday B) Tuesday C) Wednesday D) Saturday

Answer

The correct answer is D) Saturday. According to the table, Saturday has the second-lowest number of diners with 180.

Conclusion

In this article, we analyzed the data collected from several restaurants to understand the preferences of diners. We found that Thursday has the highest number of diners, while Sunday has the lowest number of diners. We also found that Friday has the second-highest number of diners, while Saturday has the second-lowest number of diners. This analysis can help restaurants to better understand their customers' preferences and make informed decisions about their business.

Mathematical Concepts

This case study involves several mathematical concepts, including:

Data analysis: The process of collecting, organizing, and interpreting data to draw meaningful conclusions.
Statistics: The study of the collection, analysis, interpretation, presentation, and organization of data.
Graphs: A visual representation of data, used to communicate information and trends.
Tables: A way of organizing data into rows and columns, used to present information in a clear and concise manner.

Real-World Applications

This case study has several real-world applications, including:

Marketing: Understanding customer preferences can help businesses to develop effective marketing strategies.
Business: Analyzing data can help businesses to make informed decisions about their operations and strategy.
Research: Data analysis is a crucial aspect of research, used to draw conclusions and make recommendations.

Future Directions

This case study can be extended in several ways, including:

Collecting more data: Collecting more data from different restaurants and locations can provide a more comprehensive understanding of diners' preferences.
Analyzing other factors: Analyzing other factors, such as time of day, location, and type of cuisine, can provide a more nuanced understanding of diners' preferences.
Developing predictive models: Developing predictive models can help businesses to forecast demand and make informed decisions about their operations.
Directions: Select the correct answer from each drop-down menu. Diners at several restaurants were surveyed to see what day of the week they prefer to go out to eat. The following table gives some of the data collected by the restaurants.

Q1: What is the day of the week with the highest number of diners?

A) Monday B) Tuesday C) Thursday D) Friday

Answer: C) Thursday. According to the table, Thursday has the highest number of diners with 200.

Q2: What is the day of the week with the lowest number of diners?

A) Monday B) Tuesday C) Wednesday D) Sunday

Answer: D) Sunday. According to the table, Sunday has the lowest number of diners with 120.

Q3: What is the day of the week with the second-highest number of diners?

A) Monday B) Tuesday C) Thursday D) Friday

Answer: D) Friday. According to the table, Friday has the second-highest number of diners with 220.

Q4: What is the day of the week with the second-lowest number of diners?

A) Monday B) Tuesday C) Wednesday D) Saturday

Answer: D) Saturday. According to the table, Saturday has the second-lowest number of diners with 180.

Q5: What is the average number of diners per day?

A) 150 B) 180 C) 200 D) 220

Answer: B) 180. To calculate the average, we add up the number of diners for each day and divide by the total number of days. (120 + 150 + 180 + 200 + 220 + 180 + 120) / 7 = 180.

Q6: What is the median number of diners per day?

A) 150 B) 180 C) 200 D) 220

Answer: B) 180. To calculate the median, we arrange the number of diners in order from smallest to largest: 120, 150, 180, 200, 220, 180, 120. The middle value is 180.

Q7: What is the mode of the number of diners per day?

A) 120 B) 150 C) 180 D) 200

Answer: C) 180. The mode is the value that appears most frequently. In this case, 180 appears twice, making it the mode.

Q8: What is the range of the number of diners per day?

A) 100 B) 120 C) 200 D) 220

Answer: D) 220. The range is the difference between the largest and smallest values. In this case, the largest value is 220 and the smallest value is 120, so the range is 220 - 120 = 100.

Q9: What is the interquartile range (IQR) of the number of diners per day?

A) 50 B) 100 C) 150 D) 200

Answer: B) 100. To calculate the IQR, we first need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, which is 150. Q3 is the median of the upper half of the data, which is 200. The IQR is Q3 - Q1 = 200 - 150 = 50.

Q10: What is the standard deviation of the number of diners per day?

A) 20 B) 30 C) 40 D) 50

Answer: C) 40. To calculate the standard deviation, we first need to calculate the variance. The variance is the average of the squared differences from the mean. The mean is 180, so the squared differences are (120 - 180)^2, (150 - 180)^2, (180 - 180)^2, (200 - 180)^2, (220 - 180)^2, (180 - 180)^2, and (120 - 180)^2. The variance is the average of these squared differences, which is 400. The standard deviation is the square root of the variance, which is √400 = 20.