Interpreting the Given Data

Oct 13, 2025 by windailys.com 112 views

Minimum: 3

Lower quartile: 14

Median: 23

Upper quartile: 29

Maximum: 40

Which box plot represents the data?

To determine which box plot represents the given data, we need to understand the characteristics of a box plot and how it is constructed. A box plot is a graphical representation of the distribution of a dataset, showing the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

Understanding the Five-Number Summary

Minimum: The smallest value in the dataset.
First Quartile (Q1): The median of the lower half of the dataset.
Median (Q2): The middle value of the dataset when it is sorted in ascending order.
Third Quartile (Q3): The median of the upper half of the dataset.
Maximum: The largest value in the dataset.

Interpreting the Given Data

Given the data:

Minimum: 3
Lower quartile (Q1): 14
Median (Q2): 23
Upper quartile (Q3): 29
Maximum: 40

We can see that the data is skewed to the right, with a long tail towards the higher values. The median is 23, which is higher than the lower quartile (14), indicating that the data is not symmetric.

Constructing a Box Plot

A box plot consists of the following components:

Box: The box represents the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
Whiskers: The whiskers represent the range of the data, extending from the minimum to the maximum value.
Median line: The median line represents the median value of the dataset.

Identifying the Correct Box Plot

Based on the given data, we can identify the correct box plot by looking for the following characteristics:

The box should be positioned at the median value (23).
The whiskers should extend from the minimum value (3) to the maximum value (40).
The box should be wider than the whiskers, indicating that the data is skewed to the right.

Conclusion

Based on the given data and the characteristics of a box plot, we can conclude that the correct box plot represents the data.

Box Plot Representation

The correct box plot representation is as follows:

The box is positioned at the median value (23).
The whiskers extend from the minimum value (3) to the maximum value (40).
The box is wider than the whiskers, indicating that the data is skewed to the right.

This box plot representation accurately depicts the distribution of the data, showing the five-number summary and the skewness of the data.

Final Answer

The correct box plot representation is the one that shows the box positioned at the median value (23), the whiskers extending from the minimum value (3) to the maximum value (40), and the box being wider than the whiskers.

This box plot accurately represents the given data, providing a clear visual representation of the distribution of the number of tables served each night at the restaurant.

Minimum: 3

Lower quartile: 14

Median: 23

Upper quartile: 29

Maximum: 40

Which box plot represents the data?

Understanding the Five-Number Summary

Minimum: The smallest value in the dataset.
First Quartile (Q1): The median of the lower half of the dataset.
Median (Q2): The middle value of the dataset when it is sorted in ascending order.
Third Quartile (Q3): The median of the upper half of the dataset.
Maximum: The largest value in the dataset.

Interpreting the Given Data

Given the data:

Minimum: 3
Lower quartile (Q1): 14
Median (Q2): 23
Upper quartile (Q3): 29
Maximum: 40

We can see that the data is skewed to the right, with a long tail towards the higher values. The median is 23, which is higher than the lower quartile (14), indicating that the data is not symmetric.

Constructing a Box Plot

A box plot consists of the following components:

Box: The box represents the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
Whiskers: The whiskers represent the range of the data, extending from the minimum to the maximum value.
Median line: The median line represents the median value of the dataset.

Identifying the Correct Box Plot

Based on the given data, we can identify the correct box plot by looking for the following characteristics:

The box should be positioned at the median value (23).
The whiskers should extend from the minimum value (3) to the maximum value (40).
The box should be wider than the whiskers, indicating that the data is skewed to the right.

Conclusion

Based on the given data and the characteristics of a box plot, we can conclude that the correct box plot represents the data.

Box Plot Representation

The correct box plot representation is as follows:

The box is positioned at the median value (23).
The whiskers extend from the minimum value (3) to the maximum value (40).
The box is wider than the whiskers, indicating that the data is skewed to the right.

This box plot representation accurately depicts the distribution of the data, showing the five-number summary and the skewness of the data.

Final Answer

This box plot accurately represents the given data, providing a clear visual representation of the distribution of the number of tables served each night at the restaurant.

Q&A

Q: What is a box plot?

A: A box plot is a graphical representation of the distribution of a dataset, showing the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

Q: What are the components of a box plot?

A: The components of a box plot are:

Box: The box represents the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
Whiskers: The whiskers represent the range of the data, extending from the minimum to the maximum value.
Median line: The median line represents the median value of the dataset.

Q: How do you identify the correct box plot?

A: To identify the correct box plot, look for the following characteristics:

The box should be positioned at the median value.
The whiskers should extend from the minimum to the maximum value.
The box should be wider than the whiskers, indicating that the data is skewed to the right.

Q: What does the box plot representation show?

A: The box plot representation shows the five-number summary and the skewness of the data.

Q: What is the final answer?

A: The final answer is the box plot representation that shows the box positioned at the median value, the whiskers extending from the minimum value to the maximum value, and the box being wider than the whiskers.

Q: What is the significance of the box plot in this context?

A: The box plot is significant in this context as it provides a clear visual representation of the distribution of the number of tables served each night at the restaurant, showing the five-number summary and the skewness of the data.

Q: Can you provide an example of a box plot?

A: Yes, the box plot representation provided earlier is an example of a box plot.

Q: How do you interpret the box plot?

A: To interpret the box plot, look for the following characteristics:

The position of the box: The box should be positioned at the median value.
The length of the whiskers: The whiskers should extend from the minimum to the maximum value.
The width of the box: The box should be wider than the whiskers, indicating that the data is skewed to the right.

Q: What are the advantages of using a box plot?

A: The advantages of using a box plot are:

It provides a clear visual representation of the distribution of the data.
It shows the five-number summary and the skewness of the data.
It is easy to interpret and understand.

Q: What are the disadvantages of using a box plot?

A: The disadvantages of using a box plot are:

It can be difficult to create a box plot for large datasets.
It may not be suitable for datasets with outliers.

Q: Can you provide a real-world example of a box plot?

A: Yes, a real-world example of a box plot is a restaurant's sales data, where the box plot can be used to show the distribution of sales over a period of time.

Q: How do you create a box plot?

A: To create a box plot, follow these steps:

Collect the data.
Calculate the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
Create the box plot using the five-number summary.

Q: What are the different types of box plots?

A: The different types of box plots are:

Simple box plot: A simple box plot shows the five-number summary.
Modified box plot: A modified box plot shows the five-number summary and the outliers.
Notched box plot: A notched box plot shows the five-number summary and the confidence interval.

Q: How do you choose the right type of box plot?

A: To choose the right type of box plot, consider the following factors:

The size of the dataset.
The presence of outliers.
The level of detail required.

Q: What are the common mistakes to avoid when creating a box plot?

A: The common mistakes to avoid when creating a box plot are:

Not calculating the five-number summary correctly.
Not using the correct type of box plot for the dataset.
Not labeling the box plot correctly.

Q: How do you troubleshoot common issues with box plots?

A: To troubleshoot common issues with box plots, follow these steps:

Check the data for errors.
Check the calculation of the five-number summary.
Check the type of box plot used.
Check the labeling of the box plot.

Q: What are the best practices for creating a box plot?

A: The best practices for creating a box plot are:

Use a clear and concise title.
Use a clear and concise axis label.
Use a clear and concise legend.
Use a clear and concise color scheme.

Q: How do you present a box plot effectively?

A: To present a box plot effectively, follow these steps:

Use a clear and concise title.
Use a clear and concise axis label.
Use a clear and concise legend.
Use a clear and concise color scheme.
Use a clear and concise font.

Q: What are the common applications of box plots?

A: The common applications of box plots are:

Data analysis: Box plots are used to analyze the distribution of data.
Data visualization: Box plots are used to visualize the distribution of data.
Data presentation: Box plots are used to present the distribution of data.

Q: How do you use box plots in data analysis?

A: To use box plots in data analysis, follow these steps:

Collect the data.
Calculate the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
Create the box plot using the five-number summary.
Interpret the box plot.

Q: What are the advantages of using box plots in data analysis?

A: The advantages of using box plots in data analysis are:

It provides a clear visual representation of the distribution of the data.
It shows the five-number summary and the skewness of the data.
It is easy to interpret and understand.