Understanding the Box Plot

Oct 13, 2025 by wbrum.org 24 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 median, quartiles, and outliers.

Understanding the Box Plot

A box plot consists of the following components:

Minimum Value: The lowest value in the dataset.
Maximum Value: The highest value in the dataset.
Lower Quartile (Q1): The median of the lower half of the dataset.
Upper Quartile (Q3): The median of the upper half of the dataset.
Median: The middle value of the dataset.

Interpreting the Given Data

Given the data, we have:

Minimum = 3
Lower Quartile (Q1) = 14
Median = 23
Upper Quartile (Q3) = 29
Maximum = 40

Constructing the Box Plot

To construct the box plot, we need to determine the position of the median, lower quartile, and upper quartile.

The median is the middle value of the dataset, which is 23.
The lower quartile (Q1) is the median of the lower half of the dataset, which is 14.
The upper quartile (Q3) is the median of the upper half of the dataset, which is 29.

Determining the Box Plot Type

Based on the given data, we can determine the type of box plot that represents the data.

If the median is close to the lower quartile, the box plot is likely to be a left-skewed box plot.
If the median is close to the upper quartile, the box plot is likely to be a right-skewed box plot.
If the median is close to the middle of the box, the box plot is likely to be a symmetric box plot.

Analyzing the Data

Based on the given data, we can see that the median (23) is close to the middle of the box. The lower quartile (14) is below the median, and the upper quartile (29) is above the median. This suggests that the box plot is likely to be a symmetric box plot.

Conclusion

Based on the given data, the box plot that represents the data is a symmetric box plot. The median is close to the middle of the box, and the lower and upper quartiles are equidistant from the median.

Box Plot Representation

Here is a representation of the box plot:

  +---------------+
  |               |
  |  3  |       |  40
  |  ---+-------+---
  |  14 |       |  29
  |  ---+-------+---
  |  23 |       |
  +---------------+

This box plot represents the given data, with the median (23) at the center, and the lower and upper quartiles (14 and 29) at the edges.